It is assumed from his name that his roots lie in the municipality of Fuenllana, in the province of Ciudad Real, although he was born in Navalcarnero, Madrid.
Blind from birth, he composed a Libro de música para vihuela intitulado Orphenica Lyra (Seville, 1554), dedicated to Philip II of Spain.
At the arrival of Isabel de Valois, third wife of Philip II, she brought with her a group of French instrumental musicians who wished to stay in the Spanish court; Fuenllana alternated with this group and his musical works were performed together with those of foreign artists.
This work also contains arrangements of vocal pieces by Josquin, Morales, Francisco Guerrero, and Philippe Verdelot, musicians from both Spain and the Low Countries.
The vocal parts are written in red ciphers, indicating which notes are to be sung while the black ones are to be played on the vihuela; alternatively, one can play the whole intabulation although it is often very demanding (e.g., Mateo Flecha's Ensalada 'La Bomba' in the Libro Sexto).