We investigated the quantum speed limit time of a non-Hermitian two-level system for which gain and loss of energy or amplitude are present. Our results show that, with respect to two distinguishable states of the non-Hermitian system, the evolutionary time does not have a nonzero lower bound. The quantum evolution of the system can be effectively accelerated by adjusting the non-Hermitian parameter, as well as the quantum speed limit time can be arbitrarily small even be zero.