Knud Moller was an apprentice painter 1896-1900. He was employed by the teatre painter August Wallin in the Dagmar teatre and 1902-1909 by Thorolf Pedersen at the painter's hall of the Royal Danish Teatre. He was employed at Bing & Grondahl in the periods 1909-1912 and 1914-1921. At Royal Copenhagen he was employed 1912-1914.
His primary subjects in porcelain have been birds. After working at the porcelain factories he became an independent sculptor, engraver and illustrator.
In the period 1910-1948 he exhibited no less than 29 times with 41 works at the Art Academy's showrooms at Charlottenborg. Until his death in 1965 he exhibited every year at Charlottenborg. He was a lifetime member of the Union for National Art.
In 1932 he received the Eckersberg medal.