The invention relates to a planetary gear box fault diagnosis method based on low-rank sparse approximation. The planetary gear box fault diagnosis method based on low-rank sparse approximation comprises the steps of: acquiring output shaft angle position signals by utilizing a built-in coder at first, then, fitting and differentiating the output shaft angle position signals by taking the mean square error as a loss function, so that instantaneous angle speed signals are obtained, on the basis of the instantaneous angle speed signals, respectively performing time-domain synchronous averaging on a planet wheel, a sun wheel and a gear ring, then, performing low-rank sparse approximation on respective time-domain synchronous averaging signals, so that sparse recovery signals of the planet wheel, the sun wheel and the gear ring are obtained, furthermore, calculating each kurtosis, and judging that the signal, the kurtosis of which is greater than a kurtosis threshold value, fails. According to the planetary gear box fault diagnosis method based on low-rank sparse approximation in the invention, by utilization of the characteristics of a low-rank sparse approximation method, acquired compound signals are decoupled; normal meshing information and fault information of a planetary gear box are separated; fault characteristics are prominent; and early weak fault diagnosis of the planetary gear box is easily realized.