The direct measurement with an angular accelerometer often brings impulse noise and Gaussian white noise when the experiments are carried out under heavy load and multi-disturbance environment. In the light of this problem, a self-adaptive de-noising algorithm which combines median filter and discrete wavelet threshold de-noising is proposed. First, the median filter is used to preprocess the original signal. Then, discrete wavelet threshold de-noising method is used to remove Gaussian white noise. It determines self-adaptively wavelet decomposition level and improves the threshold selection criterion. The simulation results indicate that this algorithm can increase the signal-to-noise ratio (SNR) and reduce the mean squared error (MSE) effectively. The experiment results show that this algorithm can remove noise in molecular circular angular accelerometer signal as well as protect high dynamic part in the real signal.