After Vitus Bering's 1741 tragic venture he was, together with Peter Kuzmich Krenitzin, among the first to conduct an expedition to Alaska and the Aleutians.
Levashev was sent by Russian Empress Catherine II, as main assistant of expedition leader Krenitzin, to explore the northern parts of the Pacific Ocean and particularly the area around the Bering Strait on four ships.
Certain geographic features of the Alaskan coast, like Avatanak and Akutan Island were named by Krenitzin and Levashev in the maps that were subsequently published.
On 4 July 1770, when Krenitzin drowned, Levashef assumed command of the Russian expedition fleet and returned to St. Petersburg, where he arrived on 22 October 1771.
Port Levashef, the harbor in Unalaska where Levashev had wintered his first year in the Northern Pacific was named in honor of this early Russian explorer by Lieutenant Gavril Sarychev.