Abstract: Gamma-ray bursts (GRBs) are luminous and violent phenomena in the universe. Traditionally, long GRBs are expected to be produced by the collapse of massive stars and associated with supernovae. However, some low-redshift long GRBs have no detection of supernova association, such as GRBs 060505, 060614 and 111005A. It is hard to classify these events convincingly according to usual classifications, and the lack of the supernova implies a non-massive star origin. We propose a new path to produce long GRBs without supernova association, the merger of a stellar-mass black hole and a white dwarf, which fills an important gap in compact binary evolution.