By solving the quantum Vlasov equation, electron–positron pair production in a strong electric field with asymmetric laser pulses has been investigated. We consider three different situations of subcycle, cycle and supercycle laser pulses. It is found that in asymmetric laser pulse field, i.e., when the pulse length of one rising or falling side is fixed while the pulse length of the other side is changed, the pair production rate and number density can be significantly modified comparable to symmetric situation. For each case of these three different cycle pulses, when one side pulse length is constant and the other side pulse length becomes shorter, i.e., the whole pulse is compressed, the more pairs can be produced than that in the vice versa case, i.e., the whole pulse is elongated. In compressed pulse case there exists an optimum pulse length ratio of asymmetric pulse lengths which makes the pair number density maximum. Moreover, the created maximum pair number density by subcycle pulse is larger than that by cycle or/and supercycle pulse. In elongated pulse case, however, only for supercycle laser pulse the created pairs is enhanced and there exists also an optimum asymmetric pulse length ratio that maximizes the pair number density. On the other hand, surprisingly, in both cases of subcycle and cycle elongated laser pulses, the pair number density is monotonically decreasing as the asymmetry of pulse increases.