Previous particle-in-cell simulations have shown that electron phase-space holes (electron holes),where the associated parallel electric field has a bipolar structure,exist near the four separatrices in anti-parallel magnetic reconnection.By performing two-dimensional (2-D) particle-in-cell (PIC) simulations,here we investigate magnetic reconnection in an asymmetric current sheet,with emphasis on the parallel electric field near the separatrices.Compared with magnetic reconnection in a symmetric current sheet,it is found that the parallel electric field with a bipolar structure only exists around the separatrices in the upper region with a lower density (upper separatrices).Such a bipolar structure of the parallel electric field is considered to be associated with electron holes resulting from the nonlinear evolution of the electron beam instability excited by the high-speed electron flow formed after their acceleration around the X line.The disappearance of the parallel electric field around the separatrices in the lower region with a higher density (lower separatrices) may be due to the transverse instability,which is unstable in a weak magnetized plasma.