The problem in the processing of mechanical fault vibration signal by variational nonlinear chirp mode decomposition（VNCMD）,the noise leads to time-frequency surface blurring,which reduces the accuracy of time-frequency ridges extracted,and then affects the decomposition effect of VNCMD,is aimed at,so a joint fault diagnosis of convex optimization and VNCMD is proposed.The noise can be eliminated by solving the sparse approximate solution of signal via the convex optimization algorithm,which can improve the readability of the time-frequency surface,so as to obtain accurate timefrequency ridges.Then,by using these ridges,the fault features of the signal can be extracted effectively via VNCMD.Through the analysis of simulated signal and the measured bearing outer ring fault data,the results demonstrate that the proposed method can realize the accurate extraction of rolling bearing fault feature.