Kantner had suffered a heart attack earlier in the week, according to Rolling Stone magazine.
The musician had been in ill health in recent years, with Kantner suffering a heart attack in March 2015.
With Jefferson Airplane, Kantner helped pioneer the oft-imitated psychedelic sound: simple, fuzzy guitar lines steeped in dreamlike reverb.
The group formed in 1965 and, within a few years, scored hits with "Somebody to Love" and "White Rabbit." In their first run, five of the band's seven albums went gold, including 1967's Surrealistic Pillow and 1968's Crown of Creation.
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Paul Lorin Kantner was born on March 17, 1941 in San Francisco. His father was a traveling salesman and he was sent to military school after his mother's death. He found inspiration in science-fiction books and folk music, dropping out of college to pursue music.
Outside of his main bands, Kantner recorded two albums with Slick and a 1983 solo record, Planet Earth Rock and Roll Orchestra. He also recorded with the KBC Band, which featured fellow Airplane members Blain and Casady.