Vasiukov was born on March 5, 1933 in Moscow. His family was evacuated to Tula during World War II, and his father died in the Battle of Kursk. He learned to play chess at the age of 15, a very late age even for that time. In 1954, he was awarded the title Master of Sports of the USSR in Chess (ru). That same year, Vasiukov represented Moscow in the Soviet Team Championship finals in Riga. He scored his first important chess success in 1955 by winning the Moscow City Championship with a score of 10½/15 points, ahead of Salo Flohr, who was second. He played in the Soviet Championship semi-final at Yerevan 1955 and finished in the middle of a powerful field.