In this research, a classifier is proposed for automatic modulation classification of some common modulation schemes, i.e., BPSK, QPSK, 8-PSK and 16-QAM. Our proposed classifier considers multipath fading effects on the received signal in a non-Gaussian noise environment. Automatic modulation classification is very challenging in real-world scenarios due to fading effects and additive Gaussian mixture noise on modulation schemes. Most of the available modulation classifiers do not consider the fading effects which results in degradation of classification in a blind channel environment. In our work, the channel is supposed to be suffering from excessive additive Gaussian mixture noise and frequency selective fading resulting in low signal SNR. The estimation of the unknown channel along with noise parameters is performed using ECM algorithm and then used in maximum-likelihood classifier for the classification of modulation schemes. Simulation results are presented that show 2 dB improvement in performance than classifier which considers only Gaussian noise in the received signal.