Aiming at incipient fault diagnosis problem of gear under strong background noise, an feature extraction method for weak fault based on maximum correlated kurtosis deconvolution and sparse code shrinkage was proposed. As the processing result of maximum correlated kurtosis deconvolution algorithm was affected by filter length parameter and deconvolution period parameter, in order to achieve the best deconvolution result adaptively, particle swarm optimization algorithm with excellent optimization characteristic was used to search for the optimal combination of influencing parameters of maximum correlated kurtosis deconvolution algorithm. The impact characteristic of original fault signal could be enhanced after processed by maximum correlated kurtosis deconvolution algorithm with optimized parameters, in order to eliminate the residual noise, the deconvolution signal was further processed by sparse code shrinkage de-noising algorithm, then fault characteristic frequency components could be identified by analyzing the envelope spectrum of de-noising signal. The analysis results verified the effectiveness and reliability of this method.