Deep learning (DL) has been applied to digital signal modulation identification (DSMI) due to its powerful feature learning ability. However, most of the existing DL-based DSMI methods are limited to specific experimental scene relating to the additive white Gaussian noise (AWGN) channel or static multipath channel. The result is that the trained network has deteriorative identification accuracy when the channel conditions change unless retrained. To solve the problem, this paper proposes a DSMI method suitable for orthogonal frequency division multiplexing (OFDM) under different multipath channels, including the variation of delay, path number and channel coefficient. This method can accurately detect the modulation feature rather than the channel's to identify the modulation type, thus reducing the network training amount. The method is divided into two parts. Firstly, traditional signal processing methods are combined, including various channel estimators and equalisers to compensate for the channel. Then a robust DL network, RSN-MI, is designed as a classifier. Unlike other DL-based DSMI methods, the influence of signal processing algorithms on DSMI performance are focused on rather than model parameters. Besides, the proposed classifier is compared with the DSMI classifier in other contributions. The results show that the classifier works better in different multipath channels.