Pasveer was born February 10, 1933 in Coevorden to a family of peat boatmen. By chance, a harmonium arrived at his home. Soon the first psalms blew through the house. When he was fifteen he became organist in the Dutch Reformed Church in Oosterhesselen in Drenthe. Two years later he conducted his first choir.
Through his lessons with Willem Hendrik Zwart, son of the Zaan organist Jan Zwart, Jan Pasveer ended up in the Zaan region. In 1953 he was appointed organist of the Reformed Zuiderkerk in Zaandam.
In 1955 he settled in Zaandam. He then became a teacher of general musical education at the VMZ, the later Gemeentelijke Muziekschool Zaanstreek. Two years later he became director. Under his leadership, music education professionalized and the music school grew substantially. The people he led knew Jan Pasveer as a sociable person, a man with an interest in others, someone who stood up for his staff and appreciated the teachers.
His musicality and personality brought him to the Amsterdam music lyceum, later the Sweelinck Conservatory, in the early 1970s. There, in addition to his job as music school director in Zaandam, he became principal study teacher in choral conducting. In 1994 he retired from the Zaanse School of Music.
Jan Pasveer has been called a "stimulating and inspiring personality" by many. He has been royally decorated twice. In 1981 he was appointed a knight in the order of Orange-Nassau, later he became an officer in the order of Orange-Nassau.
More awards came his way. For example, with the Zaans Cantatekoor he received the Culture Prize of the Municipality of Zaanstad in 1988. Another highlight with this choir was the performance of the opera 'Montag aus Licht' by the famous German composer Karlheinz Stockhausen, which was premiered at the Scala in Milan. In 2003, at the celebration of its 25th anniversary, the choir disbanded itself. At the farewell reception, it was announced that the music department of art education center Fluxus would henceforth call the annual award for up-and-coming talent the Jan Pasveer Trophy. Pasveer himself continued to play a role in awarding the trophy.
Pasveer has conducted many choirs. From 1974 until the end of 1995 he was conductor of the Christelijke Oratorium Vereniging Zaanstreek. Since 1980 he conducted the Amsterdam Westerkerk Choir.
Pasveer was extremely active in the field of church music. He served on numerous committees, including the church music committee charged with overseeing the quality of church singing. Pasveer campaigned for its modernization. In 2001 the book "Het kerklied" appeared partly under his editorship, and in the mid-1980s he began a book on symbolism in Bach's music. He planned to obtain a doctorate with this.