Strongly influenced by Kristian Zahrtmann, he painted bright, colourful landscapes while travelling in Italy.
He frequently visited the artists' colony of Skagen in the north of Denmark where he painted scenes of the dunes and beaches.
After studying at Harald Foss's technical school in Copenhagen, he entered the Royal Danish Academy of Fine Arts in 1888.
In some of his earlier works, including Bøn om Regn and Vinhøst I Abruzzerne, Wilhjelm employs a frieze-like relief style which Zahrtmann strongly discouraged.
By contrast, his bright, colourful works from Italy, above all those from Civita d'Antino such as Motiv fra en Procession i Appenninerne reveal Zahrtmann's influence.