Successive interference cancellation (SIC) is an effective multipacket reception scheme to combat interference at the physical layer. This paper studies the problem of maximizing the number of successful simultaneous transmissions (i.e., transmission capacity) in a wireless network with SIC at the physical layer. First, an interference model based on the physical interference model is proposed to characterize the sequential detection nature of SIC. Then, an algorithm is presented to evaluate whether or not a link set is feasible. Next, recognizing capacity maximization is a NP-hard problem, a novel approximation solution based on the genetic algorithm (GA) is provided. Finally, the design and parameter setting of the GA solution are discussed, and the performance is validated by various simulations.