In order to double the injection rate of positron beam from the linac to the storage ring of BEPCⅡ, a two-pulse generation and acceleration scheme has been proposed. The two-pulse simulation by programs including LIAR, PARMELA, EGUN and TRANSPORT is described first and the method is applied in the beam dynamics studies of BEPCⅡ linac. The experiment of two-pulse acceleration was performed in BEPCⅡ linac and some preliminary results are obtained, which provides a good reference for further upgrading of BEPCⅡ injector linac.