Alakbar Taghiyev was born in Ganja.

He studied at Moscow State Law University.

In 1938, he began his labor activity at the City People's Court. He worked in the prosecutor's office for 36 years (until 1974). He began writing songs in 1958 - after the birth of his son Khaliq Tagiyev. He wrote his first song "Neighboring Girl" during the years he lived in Ganja. Inspired by the success of this song, the composer quickly composed songs such as "Sweet Dreams", "You Couldn't Come", "I Couldn't Believe", "Baku Nights", and "My Azerbaijan". To receive professional musical education, he studied at the composition course at the Baku Music School named after Asaf Zeynalli (1962-1964). He was elected a member of the USSR Music Foundation. The performer of most of his first songs was Zeynab Khanlarova, and this collaboration lasted for about 10 years. He has collaborated with Nisa Gasimova since 1972. The composer's songs "You Couldn't Come", "My Daughter", "Sen'e qurban", "Sedaqatim var" have repeatedly entered the repertoire of foreign singers.

Alakbar Taghiyev died in 1981 and was buried in the "Seyidler" cemetery in Mashtaga.