The golden era of reggae and rock-steady gleamed again for two hours at the Martha’s Vineyard Performing Arts Center August 13, when Toots & the Maytals delighted their audience with a concert featuring many Jamaican hits from the 1960s and 1970s.

Now 75, Frederick (Toots) Hibbert has been making people dance for close to 60 years. He has written some of the most recognizable tunes in Jamaican music, including Pressure Drop, Sweet and Dandy and Never Grow Old, and recorded the first song to name-check the emerging musical style of the 1970s: Do the Reggay.

Along with the all-important rhythm section of bass, guitar and drums, Mr. Hibbert brought a pair of female singers and a keyboard player with synthesized horns to recreate the big-band, vocal trio sound of early ska and rock-steady on songs like Pomp & Pride and Monkey Man.

Mr. Hibbert—who reportedly is able to play every instrument in his band—also soloed on guitar several times during the evening. Coiling rhythms, body-shaking bass and funky drumming had many audience members on their feet and dancing from the beginning of the show. Fans in wheelchairs—including cast members from the previous week’s Camp Jabberwocky musical—moved to the center aisle so they could see.

Rolling Stone magazine has named Mr. Hibbert one of its 100 “best vocalists of all time,” and on Monday he showed the multi-generational audience why he’s on that list. With a voice that ranges from a low growl to the heights of gospel and soul, he often improvised during songs and even sang many of his stage remarks.

A seasoned showman, Mr. Hibbert worked the audience both between and during the band’s numbers, encouraging sing-alongs and call-and-response choruses. He also had a little good-natured fun with the crowd.

“Tonight I am going to be your teacher and every one of you are my students,” he crooned, before leading listeners through a tongue-twisting series of vocal sounds.

“Don’t you know that you are very beautiful?” he said, as the crowd applauded happily after Never Grow Old. “And we on stage are so beautiful too,” he added slyly, to more applause and cheers.

Along with more than a dozen of his classic 1960s and 1970s tunes, Mr. Hibbert introduced the audience to his new song Marley, which he debuted on the Tonight Show late last month. A tribute to Jamaica’s most famous musician, the late Bob Marley, it will be released commercially later this month, Mr. Hibbert said.

The love song I Know gave Mr. Hibbert the chance to get close to his listeners.

“You know who I am, I want to know who you are,” he sang at the edge of the stage, clasping hands with one eager fan after another. “Hello, hello, you make me feel irie.”

The audience needed no invitation to sing along when the band played Richard Berry’s party anthem Louie Louie, and went wild with joy for Mr. Hibbert’s hit reggae version of John Denver’s Take Me Home Country Roads.

“Did I give you a night to remember?” Mr. Hibbert asked near the end of the show.

“Yes!” roared the Vineyard audience.

Monday’s performance was presented by the Martha’s Vineyard Concert Series.