Born in Aarhus, Møldrup grew up as an only child in Nørregade, in the inner city, in a music loving workers family.
He started apprenticeship as a mason, like his father, but soon fell in love with the guitar.
[4] Later on, at the Danish Royal Academy of Music in Aarhus, Møldrup received his initial training under Jytte Gorki Schmidt, obtaining his academy diploma in 1972.
He played repertoire from all periods — Renaissance, Baroque, Classical, 'Segovia-style' and modern — and he commissioned a large number of works from living Scandinavian composers (see below).
Møldrup also authored the book "Guitaren, et eksotisk instrument i den danske musik" (The Guitar, an exotic instrument in Danish music) and a number of articles.