In view of the multi-component coupling modulation characteristics of complex fault signals and the envelope error phenomenon of the local average decomposition method,an LMD method based on rational sub-interval Hermite interpolation is proposed. Through calculating the optimal parameter interval,the optimal parameter between the cells and the parameter in the optimal parameter interval is selected to adjust the shape of the interpolation spline so that the interpolation spline is infinitely close to the target to be interpolated,thereby improving the fitting precision and accuracy of the envelope curve. The comparison of simulation data is used to verify the approximation ability and high fitting accuracy of the rational Hermite interpolation LMD method. The method is applied to the diagnosis of compound fault signals of gear and rolling bearing,and the high fitting accuracy of the method is proved again. The accurate diagnosis of compound fault signal is realized.