Brojen was born in the Kuchiamora village of Bikrampur, Bangladesh. On his initiative, the East Pakistan Sports Federation introduced an annual swimming competition in Dhaka in 1953.
He was invited to take part in the Billy Butlin English Channel Swimming Competition in 1958. As a part of his training he swam the Shitalakshya River, a distance of 46 miles starting from Narayanganj to Chandpur. Prior to the Channel competition, he also swam the Mediterranean from Capri to Naples.He won the Channel race in August 1958
Brojen crossed the English Channel a total of 6 times from 1958 to 1961.