A love relationship between a Libra and a Virgo is quite unlikely. Libra is cardinal air and Virgo is mutable earth, this combination turns into dust. Librans are easygoing by nature and Virgos can turn out to be too much of a critic for them. In this relationship flexible practicality meets aggressive thought. Librans by the intrinsic nature of their sun sign want to create a balanced relationship of give and take. While Virgos focus on organizing the entire environment with their meticulous planning details. Libra wants harmonious and tension free environment at home while Virgo goes on organizing and reorganizing the most practical way of doing things around the house. Virgo sometimes set very high standards through their way of critical encouragement and dictatorial tendency for Librans whose philosophy in love relationship is about equality - discussing problems together and work out a reasonable and equitable solution. Virgos are more interested in money, than in sex. They are quite straightforward about their approach to sex and find Librans as social butterflies seeking pleasure. Librans are social animals while Virgos like to stay home.
However, not everything is negative in this love relationship. Virgo's quiet temperament can easily be balanced by an outgoing Libran. There can be an excellent love of friendship and frank communication between the two. Virgo can become too critical sometimes and have tendency to throw tantrums and Librans are quite capable of handling such situations with ease. If you go by their symbol which is the scale of justice, Librans always listen to both the sides of the story and then only come to a conclusion.
All in all, Virgo love compatibility with Libra is doubtful.