His music includes works for instruments (three symphonies), the church (the motet Jesus und Nikodemus, the Missa Dona nobis pacem), and collections including the Spandauer Chorbuch (Spandau choir book) and the three volume Großes Orgelbuch (Great Organ Book), which provides pieces for the entire liturgical year.

From 1922 to 1926 he studied composition at the Berliner Hochschule für Musik with Walter Gmeindl [de], a pupil of Franz Schreker.

[2] In 1934, Pepping accepted a position as teacher of harmony, sight-reading and counterpoint at the Spandauer Kirchenmusikschule of the Protestant Johannesstift Berlin [de] in Spandau, where he lived until his death.

[5] During World War II, even during its final phase, Pepping was included in the Gottbegnadeten list of artists deemed crucial to the art of the Third Reich, and was therefore exempted from military service.

Pepping based his church music on Protestant hymns, the vocal polyphony of the 16th and 17th century and modal keys.

Pepping composed no more church music until 1948, when he wrote the Missa Dona nobis pacem, possibly as a "personal plea".

The Passionsbericht des Matthäus (Passion report of Matthew) was performed in 1992 by the Danish National Radio Choir, conducted by Stefan Parkman.

All three symphonies and the piano concerto were recorded by the Nordwestdeutsche Philharmonie, conducted by Werner Andreas Albert with the pianist Volker Banfield in 2006.