Thermally stimulated conductivity (TSC) theory based on multiple trapping(MT) model in amorphous semiconductors is limited to explain TSC in a-Si: H at low temperatures in which the low temperature peak of TSC σTSC( TM) is independent of the starting temperature T0. TM is pinked. In this paper, a model of the hopping conduction with the transport energy Et in the band tail is proposed to understand the behavior of the low temperature TSC. Hopping frequency, thermal emission rate and temperature dependence of Et were calculated. TM is suggested to be corresponding to a change of the transport mechanism from hopping conduction to MT model.