The magnetohydrodynamic angular rate sensor (MHD ARS) is a high-bandwidth, high-accuracy sensor that is increasingly used to measure spacecraft harmonic vibration. However, the amplitude of harmonic vibration is usually on the order of microradian to milliradian, and the induced electric potential signal of MHD ARS is only on the order of nanovolt to microvolt, which is easily disturbed by noise. In this paper, an improved method based on autocorrelation with Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Wavelet Threshold Denoising (WTD) is proposed to denoise the signal of MHD ARS. Firstly, CEEMDAN is used to decompose noisy signals and obtain intrinsic mode functions (IMFs), and autocorrelation is used to determine the relevant modes where the effective signals are located. Then, the improved threshold and thresholding function are used to denoise the relevant modes. Finally, the denoised signal is obtained by combining the denoised relevant modes. In the experiment, noisy MHD ARS signals were recorded in static and dynamic conditions, and the effects of the proposed method and conventional methods were compared. The results of the Allan variance in the static condition and root-mean-square error in the dynamic condition show that the proposed method can effectively overcome the shortcomings of conventional methods and obtain a better denoising effect.