Aleksey Turishchev was born on March 1 (13), 1888, in Kaluga to a working-class family with many children. From childhood, he exhibited outstanding musical abilities, which allowed him to become a student of the Moscow (12th Astrakhan Grenadier) regiment and enroll in the Moscow Conservatory in the clarinet class.

In 1904, he won a competition for the best song-march for a ceremonial reception organized by Emperor Nicholas II in honor of the officers and sailors of the cruiser "Varyag" and the gunboat "Koreets." Turishchev wrote music to the poem by Rudolf Greintz, translated by Evgeniya Studenskaya, "Our proud 'Varyag' does not surrender to the enemy," arranged it for wind orchestra and choir, and conducted the first performance of "Varyag" at the Kursk railway station.

In 1910, Aleksey Turishchev graduated from the Moscow Conservatory. In 1912, he became the conductor of the 177th Izborsk Infantry Regiment in Penza and opened a clarinet class at the Penza Music School.

Aleksey Sergeyevich Turishchev participated in World War I and the Civil War. From January 1918, he served in the Red Army as the conductor of the 1st Penza Soviet Regiment.

In 1918 and 1957, he taught wind instruments at the Penza Music School and Music School No. 1, which were located in the same building. At different times, he held several positions, including director of the school and music school (in 1925 and 1935) and head of the educational department.

In 1936, he served as the conductor of the 93rd Rifle Don Regiment for nine months. During the Great Patriotic War, he took care of the evacuated students of the Central Music School at the Moscow Conservatory in Penza for four years.

Aleksey Sergeyevich Turishchev passed away on February 16, 1962, and was buried in Penza at the Mitrofanovskoye Cemetery.