Automatic modulation classification (AMC) is to identify the modulation format of the received signal corrupted by the channel effects and noise. Most existing works focus on the impact of noise while relatively little attention has been paid to the impact of channel effects. However, the instability posed by multipath fading channels leads to significant performance degradation. To mitigate the adverse effects of the multipath channel, we propose a channel-robust modulation classification framework named companding spectral quotient cumulant classification (CSQCC) for orthogonal frequency division multiplexing (OFDM) systems. Specifically, we first transform the received signal to the companding spectral quotient (CSQ) sequence by spectral circular shift division operations and modified $\text{-}$ sigmoid function mapping. Secondly, we extract the companding spectral quotient cumulants (CSQCs) from the CSQ sequence. At last, the CSQCs serve as the inputs to train the artificial neural network (ANN) classifier and use the trained ANN to make the final decisions. Notably, the classifier is only trained using the data under the Additive White Gaussian Noise (AWGN) channel condition but tested under Rician multipath fading channel. Simulation results show that the proposed CSQCC method performs robust and superior classification performance when subjected to unknown Rician multipath fading channels, in comparison to other methods. Specifically, the proposed CSQCC method achieves nearly 100% classification accuracy at the signal-to-noise ratio (SNR) of 4 dB when testing under multiple channels but only training under AWGN channel.