Leviev was a member of the innovative Plovdiv School of the 1960s - a group which also included Encho Pironkov, George Bozhilov, Dimitar Kirov, Kolyo Vitkowski and Hristo Stefanov, known as the "April Generation".
From 1970 onwards, he held numerous solo exhibitions in Plovdiv, Sofia, Varna and abroad, including in Warsaw, Prague and Los Angeles.
In 1958 he graduated in monumental and decorative painting at the National Art Academy in Sofia in the class of Professor Georgi Bogdanov.
A jubilee exhibition of paintings and drawings was held in 1984 in the Old Town, Plovdiv, and shown again in 1985 at the Shipka Six Gallery in Sofia.
In 1984, he spent two months in Paris on a grant from the Union of Bulgarian Artists, at the Cité internationale des arts.
In addition, in his earlier career Leviev did scenography for opera productions, including "Antigone 43" by Lyubomir Pipkov, "July Night" and "Knight" by Parashkev Hadzhiev, "Pagliacci" by Ruggiero Leoncavallo, and the ballet "Love Magic" by Manuel de Falla, and "The Fair in Plovdiv" by Jules Levy.