Victoria's portrait was a present for Albert. Picture from the Royal Collection
The rarely displayed portrait, by FX Winterhalter, shows the queen leaning against a red cushion with her hair half unravelled from its fashionable knot.
Victoria commissioned the painting for Prince Albert's 24th birthday as a surprise and refers to it in her journal as "my darling Albert's favourite picture".
It shows the queen was once a lively, romantic and open-minded young woman, say the exhibition organisers.
Florinda, one of a group of beautiful women. Picture from the Royal CollectionThe portrait is on display as part of the Victoria & Albert: Art & Love exhibition which runs from March 19 to the end of October.
Another, by the same German artist, shows Florinda and her companions preparing to bathe, unaware that they are being watched by King Rodrigo from the bushes nearby.
The picture was inspired by the Spanish legend set in medieval Spain. According to the legend, it was the king's jealousy that led to the Moorish invasion of Spain.
The painting, along with several others in the exhibition, also dispels the idea that the Queen disapproved of nudity in art.
Victoria herself bought the painting as a birthday gift for Prince Albert, saying: "It is a most lovely picture containing a group of beautiful women."
The happy couple had nine children. Picture from the Royal CollectionThe exhibition, being staged in The Gallery at Buckingham Palace, displays 400 works from the couple's collection, including paintings, drawings, photographs, jewellery and sculpture.
It concentrates on the monarch's love life, from her engagement to Prince Albert in 1839 until his death in 1861.
The couple used art and beautiful things as an expression of love - their enthusiastic collecting was on a scale unique among members of the British Royal Family.
"Collecting was central to their relationship," a spokeswoman told Sky News Online. "It tells a different story of Victoria to the one that so many people imagine."