The election has attracted unprecedented attention, with several prominent politicians and businessmen campaigning, drawn by the higher profile the city on the Black Sea is now receiving and the promise of several billions of dollars of Government money as it prepares to host the 2014 Games.
Volchkova said: "I feel I have responsibility, strength, and potential.
"I have not sought approval from the authorities, from the Kremlin, and I will say only one thing: whatever the result of the election, I feel responsible for this city."
She pledged to work to solve the key problems facing the city, including sea pollution and the ageing electricity supply system.
Volochkova danced with the Bolshoi Ballet in Moscow for two years before being forced to leave after her partners complained she was overweight.
In 2001 she worked with Derek Dean and Alberto Alonso in the English National Ballet.
The following year, she returned to the Bolshoi and was awarded the prestigious Prix Benois de la Danse,
Volochkova, now 32, is a notorious figure in Russia, appearing regularly in fashion magazines, tabloids and on talk shows.
Other high-profile candidates running for Mayor include opposition politician Boris Nemtsov, and tycoon Alexander Lebedev, who owns the London Evening Standard.
On Monday, Nemtsov, who was born in Sochi, was attacked with liquid ammonia outside his campaign headquarters by a group of youths that he said were pro-Kremlin activists.
Andrei Lugovoi, the former KGB officer, accused by Britain of murdering dissident Alexander Litvenenko, had earlier planned to run for mayor, but withdrew his candidacy.
His party, the ultra-nationalist LDPR, put forward on Thursday Alexei Kolesnikov, a local lawyer, as its candidate.
The official candidate of the pro-Kremlin United Russia Party is Anatoly Pakhomov, currently the city's acting Mayor.
