Bachchan, 73, played the titular character of the most wanted criminal in the movie, which also starred Zeenat Aman and Pran in pivotal roles.
"DON completes several years... And what a masterpiece it was... For me just another day of apprehensions!," he posted on Twitter.
"Don" was the third-highest grossing Bollywood movie of 1978. A remake and sequel were also released in 2006 and 2011, respectively that saw Shah Rukh Khan stepping into the shoes of Bachchan.
The "Piku" star is currently in the capital to shoot filmmaker Shoojit Sircar's next production venture, tentatively titled "Eve".
"First day works, first day anxiety, first day fathoming, first day uncertainties, first day several tries for perfection, first day in a million suggestions and first day complete...