Grigorii Brusser was born on July 25, 1898 in Moscow. His father was an employee. Grigorii studied at a high school as an external student.
In 1918, when he was a student at the Smolensk Artillery School, Brusser took part in the defense of Petrograd from German attack. After the Russian civil war, he commander various artillery subunits. He worked for the organization Plenbezh, that was occupied with the return of prisoners and refugees after World War I. After graduating from the Frunze Military Academy in 1934, he became commander of an artillery regiment.
At the beginning of the Soviet-German war, as a lieutenant-colonel, Brusser commanded the artillery of a division of the Narodnoe opolchenie (a kind of national guard). In the winter of 1942, during the harshest period of the blockade of Leningrad, when shells were exploding on its streets every day and residents who remained in the city were given rations of 125 grams of bread per day, Colonel Brusser was appointed chief of staff of army artillery. His responsibilities included locating enemy artillery batteries that were firing on the city and destroying them. Shmuel Persov wrote the following in an article about Brusser that was prepared to be sent to the Jewish press in the West: "In this complicated and responsible work the military capabilities of Grigorii Brusser were especially evident: his many years of experience and excellent theoretical background." According to his fellow officers Persov wrote, "he was a person of exceptional capacity for work, of unusual patience, and he had an iron will and a clear mind."
In November 1943, with the rank of Colonel, Grigorii Brusser became the commander of the artillery staff of the whole Leningrad Front. He took part in the planning and conduct of the operation to free Leningrad from Hitler's blockade, that ended on January 27, 1944.
In March of that year he was promoted to the rank of major-general. After the liberation of Leningrad, he participated in battles in Karelia and Estonia. During the course of the war Brusser was awarded the Order of the Red Banner (twice), and the Orders of Suvorov and Kutuzov, both 2nd class.
After the war Major-General Brusser served a chief of staff of artillery of the Leningrad Military District. He retired from military service in 1951.
Grigorii Brusser died in Leningrad in 1960.