Filipp Matveyevich was born in 1857. After receiving a secondary education, he served in the Russian Imperial Army and, after retiring with the rank of ensign, took up contracting work. He built the ataman's palace, which was consecrated on December 6, 1894, and his name became known in Ekaterinodar due to the successful completion of this large three-story building on time.

Continuing with contracting work, Akulov built an iron bridge over the Belaya River leading to the Tula stanitsa. On April 14, 1912, he, along with other wealthy residents of Ekaterinodar, opened a private pawnshop. He was elected a member of the Ekaterinodar City Duma and headed the finance committee. Akulov was also an honorary justice of the peace and an honorary member of the Military Shelter for Girls.

His merits were highly appreciated by both the city administration and military leadership: Filipp Matveyevich received the rank of collegiate assessor and the title of personal nobleman.

Filipp Matveyevich first ran for the position of city mayor in 1907. In 1916, his candidacy was proposed again, but it was only three years later that he was elected head of the city. In the elections on November 12, 1919, receiving 52 votes, Akulov became the mayor of Ekaterinodar.

In the winter of 1919-1920, the situation on the fronts of the Civil War changed in favor of the Red Army. The political situation in Ekaterinodar was complicated, and in the midst of panic, Akulov was unable to take useful actions for the city. Before the arrival of the Reds, his wife and four children were evacuated from Novorossiysk to the Princes' Islands. Filipp Matveyevich himself found himself in Crimea with the retreating White Army and then moved to Constantinople, where he was involved in supplying the Russian army of General Wrangel. In exile, he lived in Yugoslavia and passed away in the suburb of Belgrade, the city of Pancevo, on January 8, 1934.