This paper proposes a fault diagnosis method for bearing and misalignment composite faults based on servo motor speed signals. First， the change of the motor speed caused by compound fault excitation is discussed， and the theoretical feasibility of realizing compound fault diagnosis by the speed method is analyzed. Experiments show that the detection of weak fault signals such as bearings in compound faults is easily disturbed by mismatched installation faults， which makes traditional diagnosis algorithms ineffective. Second， the preprocessed speed signal and the signal obtained by FFT are passed through a recurrent neural network（RNN）， and the input time-domain features and frequency-domain features are fused together as the basis for fault classification. This time-frequency feature compound-RNN model （TFFC-RNN） can classify bearing faults and normal signals under the interference of misalignment faults with an accuracy of more than 90%. Finally， the influence of each RNN variant on the accuracy of the model is studied. The experimental results show that the feature extraction of the frequency domain part using the gated recurrent unit has the highest diagnostic accuracy of the model.