Automatic modulation classification (AMC) is a classical topic in the signal classification field and is often performed when the modulation type is adaptive. For typical modulation types such as M-PSK and M-QAM, the fourth-order cumulant statistics are usually used for modulation classification. Besides, it is also known that the AMC performance can be seriously degraded by the effects of multipath fading in wireless channels when compared with the ideal white Gaussian noise channel. In this study, a new modulation classification method is proposed, exploring different features of normalised fourth-order cumulant statistics for a modified blind channel estimation method in the multipath fading channel. The relationship between the cumulants of the received signal and the multipath fading effects is established to cope with the channel impulse response in the new algorithm. Simulation results show that the performance of the proposed AMC method is much improved than that of previously proposed ones in terms of the probability of correct classification.