Napoléon Coste was born in Amondans (Doubs), France, near Besançon. He was first taught the guitar by his mother, an accomplished player. As a teenager he became a teacher of the instrument and appeared in many concerts in the Franche-Comté. In 1829, at the age of 24, he moved to Paris where he studied under Fernando Sor and quickly established himself as the leading French virtuoso guitarist. However, the demand for guitarists was in decline and, though his brilliance provided financial stability, he failed to find a publisher for his music. As such, he had to fund its publication himself.
Coste broke his arm in 1863 as a result of an accident, which brought his performing career to a premature end. He hired an assistant and continued to teach guitar and composition. After Sor's death, Coste edited and republished Sor's original method for guitar as "Méthode complète pour la Guitare par Ferdinand Sor, rédigée et augmentée [refingered and expanded] de nombreux exemples et leçons par N. Coste".
Coste was a member of the masonic lodge Les Frères Unis Inséparables.
Napoléon Coste had a special fondness for playing on a seven-string guitar. He is known as one of the first composers to transcribe guitar music of the 17th century into modern musical notation. He died at age 77 leaving a significant catalogue of original compositions.