Aníbal Lima was born in Lamego. He studied at the Fundação Musical dos Amigos das Crianças, at the National Conservatory, Lisbon, with Herbert Zils, and at the Estoril International Music Courses, with Sandor Vegh. He is a founding member of the Lisbon String Quartet, a group distinguished in 1972 with the 1st Prize of the Guilhermina Suggia Competition. He received a scholarship from the government of the former Soviet Union to study at the Odessa Conservatory (Professor Alexander Stanko) and the Moscow Tchaikovsky Conservatory (Professor Sergei Kravechenko), where he graduated in 1980. In 1983, he won 2nd prize in the Villa-Lobos International Competition. He was the leader of the second violins of the Gulbenkian Orchestra in the 70s.