Modulation classification is a key technology in current wireless communication systems. The technology is used to find the modulation employed or estimate channel state information (CSI). In this paper, a modulation classification method is proposed for phase shift keying (PSK) and quadrature amplitude modulation (QAM) under an unknown signal-to-noise ratio (SNR) condition. The method works without carrier synchronization and is based on likelihood estimation using the probability density function (pdf) of the received signal envelope. The superior classification error rate of the proposed method is demonstrated by computer simulations.