Inspired by quantum theory, a quantum denoising method is proposed based on an adaptive Laplace statistical model and successfully applied in mechanical fault diagnosis. To enhance the adaptability of the statistical model, a Laplace probability density function with an adaptive parameter is developed. The wavelet coefficient shrinkage function is derived from Bayesian estimation theory. By integrating the inter-scale dependency of coefficients, the quantum superposition-inspired probability of signal and noise is presented. Then, variance is deduced based on quantum superposition-inspired parameters estimation to implement nonlinear shrinkage for the wavelet coefficients. This algorithm is analyzed by simulation and certificated by the bearing fault diagnosis example. Analysis results show that this algorithm has good noise reduction effects and can efficiently reduce the noise of the mechanical fault signal.