A major objective for constructing gene regulatory networks is to use them as models for designing optimal therapeutic intervention policies within the context of synchronous or asynchronous probabilistic Boolean networks (PBNs). However, most of the previous works focused on the former and only few studied the latter. This paper deals with an optimal control problem in a generalized asynchronous PBN by applying the theory of controlled semi-Markov processes. Specifically, we first describe a control model for a generalized asynchronous PBN as a controlled semi- Markov process model and then solve the corresponding optimal control problem such that the probability that the network reaches a prescribed reward level during a first passage time to some target set is maximal. Numerical examples are then given to demonstrate the effectiveness of the proposed methods.