Effects of pulse temporal profile on electron injection and trapping in the electron bow-wave injection regime are investigated by two-dimensional particle-in-cell simulations. It is found that a positive skew pulse can enhance the wake-field amplitude, extends the accelerating aera, and improves the initial velocity of electrons injected into the bubble. Thus more energetic electrons are driven into the bubble accelerating phase. The total injection number for a positive skew pulse is higher than those of negative skew and usual Gaussian pulses in the same conditions, and the quality of electron beam is also improved. The obtained result is very important and beneficial for the future experimental investigation of the laser wake-field acceleration to obtain an energetic electron beam with a large charge quantity.