Multi-fault detection of the rolling element bearing under time-varying rotational speed presents a challenging issue due to its complexity, disproportion and interaction. Computed order analysis (COA) is one of the most effective approaches to remove the influences of speed fluctuation, and detect all the features of multi-fault. However, many interference components in the envelope order spectrum may lead to false diagnosis results, in addition, the deficiencies of computational accuracy and efficiency also cannot be neglected. To address these issues, a novel method for compound faults detection of rolling element bearing based on the generalized demodulation (GD) algorithm is proposed in this paper. The main idea of the proposed method is to exploit the unique property of the generalized demodulation algorithm in transforming an interested instantaneous frequency trajectory of compound faults bearing signal into a line paralleling to the time axis, and then the FFT algorithm can be directly applied to the transformed signal. This novel method does not need angular resampling algorithm which is the key step of the computed order analysis, and is hence free from the deficiencies of computational error and efficiency. On the other hand, it only acts on the instantaneous fault characteristic frequency trends in envelope signal of multi-fault bearing which include rich fault information, and is hence free from irrelevant items interferences. Both simulated and experimental faulty bearing signal analysis validate that the proposed method is effective and reliable on the compound faults detection of rolling element bearing under variable rotational speed conditions. The comprehensive comparison with the computed order analysis further shows that the proposed method produces higher accurate results in less computation time.