Aiming at chaotic signal noise reduction with low signal-to-noise ratio and unknown dynamic system parameters, a new chaotic signal noise reduction algorithm (TQWT-ISVD), which combines tunable Q-factor wavelet transform (TQWT) and improved singular value decomposition (ISVD), is proposed. The chaotic signal with noise is decomposed by TQWT, and the subband of TQWT is divided into signal subband and noise subband according to maximum wave entropy theory and energy threshold rule. For the noise subband, ISVD is used to reduce its noise to achieve the purpose of initial noise reduction. In ISVD, the effective reconstruction order is determined by the standard deviation of the singular value subset to improve the noise suppression effect. In order to further remove noise, the signal after initial noise reduction is reconstructed by TQWT, and the reconstructed signal is denoised again by ISVD, and the chaotic signal after secondary noise reduction is obtained. TQWT-ISVD was used to denoise Lorenz simulation signal and measured sunspot number sequence. Compared with SVD method, TQWT method, complete ensemble empirical mode decomposition with adaptive noise and threshold denoising method (CEEMDAN-WT) method and modified ensemble empirical mode decomposition combined with least squares denoising method (MEEMD-LMS) method, the experimental results show that TQWT-ISVD method can denoise chaotic signals more effectively. Compared with CEEMDAN-WT method, which has the best noise reduction effect, after Lorenz signal noise reduction, the signal-to-noise ratio (SNR) of the proposed method is increased by 2.653 7%, the root mean square error (RMSE) is decreased by 19.202 4%, and the permutation entropy (PE) is decreased by 4.975 7%. After the denoising of the lunar sunspot signal, the correlation coefficient of the method is increased by 1.531 7%, and the PE is decreased by 19.877 5%.