To study the modulation classification problem for M-ary quadrature amplitude modulation (QAM) signals traveled slowly over Rayleigh and Rician fading channels, a new algorithm based on equal gain combining is proposed in the paper. The equal gain diversity model for modulation classification is given in which equal gain combining is used to combine the signals received by multiple antennas. The normalized fourth-order cumulents of the signal at the output of the combiner are estimated, which can be used as modulation classification features. The theoretical values of the normalized fourth-order cumulents of the signal at the output of the combiner for various constellations are derived as the classification criterions. The computational complexity of the developed algorithm is order N, where N is the number of the complex base-band data samples. The theoretical arguments and the practicability of the algorithm are verified via extensive simulations and comparisons with the existing approaches.