His younger brother Wilhelm was a colonel of the Polish Army, murdered by the NKVD in the Katyn massacre.
After graduation from a high school in Minsk, Paszkiewicz joined the Military School in Vilna.
In 1914–1917 he fought in the Russian Army, and then joined Polish I Corps in Russia, in which he was company leader of the 3rd Rifles Regiment.
He fought in the Polish-Soviet War in the area of Lwów and Stryj, as commandant of the 55th Infantry Regiment.
In 1923–24, Paszkiewicz attended Wyzsza Szkola Wojenna in Warsaw, after which he was promoted to the rank of officer in the Polish General Staff.
In 1924–1926, Paszkiewicz commanded Officer School of Infantry in Warsaw, and in October 1926 was named commandant of divisional infantry at 24th Infantry Division, stationed in Jaroslaw.
On 12 October 1935 Paszkiewicz was named commandant of the 12th Infantry Division from Tarnopol.
In the Invasion of Poland, the 12th Division belonged to Prusy Army, and was destroyed in the Battle of Radom.
Paszkiewicz managed to get out of German encirclement, to reach Wlodzimierz Wolynski on 13 September 1939.
Two days later he was named deputy commandant of Karpaty Army.
Twice wounded, Paszkiewicz left Poland for Romania, where he was interned.
From 1 December 1939 until 23 June 1940 he was deputy of Minister Kazimierz Sosnkowski in the government of Wladyslaw Sikorski.
In 1940, Paszkiewicz reached France, but after its collapse, he had to flee to Great Britain.
In the Polish Armed Forces in the West, he commanded 1st Rifle Brigade (October 1940 - May 1942), 4th Rifle Division (May - October 1942), 2nd Independent Armoured Brigade (October 1942 - June 1943), and then was deputy of the I Corps in the West.
On 18 December 1945 Gustaw Paszkiewicz returned to Poland, and on 15 January 1946 he joined the Polish People's Army.
Soon afterwards, he was appointed commandant of the 16th Infantry Division from Bialystok, as well as head of local security office, which coordinated the operations against anti-Communist guerillas (Cursed soldiers).
From 18 October 1946 until 14 October 1948 Paszkiewicz commanded Warsaw Military District, after which he worked at the Ministry of Forestry and was an envoy to the Sejm.
Paszkiewicz died on 27 February 1955 in Warsaw, and was buried at the Powazki Cemetery.