It is well known that the maximal success probability of the binary quantum communication can be improved by using a sub-Poissonian non-standard coherent state as an information carrier. In the present article, we consider the quantum communication with N -ary phase shift keying (N -PSK) signal for an arbitrary positive integer N > 1. By using non-standard coherent state, we analytically provide the maximal success probability of the quantum communication with N -PSK. Unlike the binary case, we show that even super-Poissonianity of non-standard coherent state can improve the maximal success probability of N -PSK quantum communication.