You might never get past Woody Harrelson’s terribly unconvincing thick makeup and prosthetics and hairpiece in “LBJ,” which serve to make him look nothing like LBJ but exactly like Woody Harrelson wearing thick makeup and prosthetics and a hairpiece.

It took two or maybe even three scenes for me to shake it off and settle in to Harrelson’s excellent performance as Lyndon Baines Johnson in veteran director Rob Reiner’s conventional but absorbing biopic about one of the most fascinating and influential figures of the 20th century.

But we got there.

“LBJ” arrives just a few months after HBO’s “All the Way,” which was based on the Broadway play of the same name. (Bryan Cranston — who achieved a remarkable physical resemblance to LBJ — was magnificent as Johnson in both productions, winning a Tony and scoring an Emmy nomination.) It covers some of the same turf as the HBO film, but casts a slightly more expansive chronological net.

We begin with President John F. Kennedy and Vice President Lyndon Johnson arriving at Love Field Airport in Dallas in November 1963 — but soon we’re back in the summer of 1960, when Johnson was JFK’s rival for the Democratic nomination but lost out, in no small part because Kennedy was the far more handsome, far more media-friendly, far more publicly affable personality than Johnson.

As LBJ puts it, Kennedy was a show horse and Johnson was a workhorse. In Johnson’s view, what the party needed was a workhorse, but the show horse dazzled ’em. After Kennedy wins the nomination, he privately acknowledges to Johnson the Texan is far more qualified to be president — but hey, how about taking the VP job, wouldn’t that be swell?

Jeffrey Donovan, probably the 100th actor (or maybe the number is closer to 200) to portray John F. Kennedy, is effective and nimble in a relatively small part. LBJ wants to loathe JFK, but Kennedy is so disarming and self-deprecating and smooth (and genuinely committed to leveling the playing field for all Americans), even the crusty Johnson has a grudging admiration for him.

As for Robert Kennedy: He and LBJ detested one another, and at least in this telling of the tale, we can easily see why Johnson thought RFK was a little, um, snot. (Michael Stahl-David does fine work as the pugnacious Bobby.)

Jennifer Jason Leigh isn’t an actress I’d immediately think of if I were casting the part of Lady Bird Johnson, but that would be short-sighted on my part because Leigh has consistently demonstrated her versatility over the years, and she delivers a spot-on performance as LBJ’s fiercely loyal and loving wife. Lady Bird understands what makes Lyndon tick far better than any of his cronies or staffers. Whereas most men — even men of considerable power and stature — could be intimidated by LBJ’s ferocious temper and famous impatience with the slightest hint of incompetence, Lady Bird nurses him through his moments of doubt and insecurity.

Much of “LBJ” centers on backroom maneuverings. Few politicians of the time could match Johnson’s ability to work a room — and another room across the hall at the same time. The invaluable character actor Richard Jenkins plays Georgia Sen. Richard Russell, who fully expects an old-boy Texan such as Johnson to stand with him in support of racist, segregationist policies — only to be blindsided when LBJ makes it his mission to carry on JFK’s visions for civil rights legislation.

Working with what appears to be medium-low budget, director Reiner does a fine job of capturing the look and feel of the early 1960s. (The makeup job on Harrelson is all the more distracting because everyone else looks just fine. Makeup, hair, wardrobe — quite excellent in every other case.)

Woody Harrelson is 56, which is actually a year older than LBJ was when he was sworn in as our 36th president on Nov. 22, 1963. Yet Harrelson generally has such a youthful and energetic onscreen persona, which would seem to be at odds with playing an imposing figure that looked like he was 60 even when was 40. It’s a well-calibrated performance, with Harrelson convincingly conveying how Lyndon Johnson felt the weight of the world on his shoulders and took on that challenge in mostly admirable ways.

★★★

Electric Entertainment presents a film directed by Rob Reiner and written by Joey Hartstone. Rated R (for language). Running time: 97 minutes. Opens Friday at local theaters.