Engine fault detection is critical to enhancing the reliability of modern equipment. However, it is challenging to obtain a large number of high-quality labeled data for engines, which is not conducive to improving the training accuracy of deep learning methods. Therefore, this article proposes a fault detection method combining adaptive recursive variational mode decomposition (ARVMD) and component energy distribution spectrum (CEDS). The paper first introduces recursive mode into VMD. Then, the mode number is dynamically selected according to the energy distribution of the power spectral density to extract the intrinsic mode functions (IMFs) continuously. The quadratic penalty term is optimized correspondingly using SNR. The decomposition results of artificial and real signals demonstrated that ARVMD has higher SNR and efficiency than VMD. Next, the center frequency and unit bandwidth energy of IMF are used to construct CEDS. Fault diagnosis is realized by the CEDS correlation ranking of various faults. Finally, two case studies are performed to illustrate the effectiveness of the proposed method. The results show that the proposed ARVMD-CEDS method provides an efficient and effective solution for single-channel engine fault diagnosis.