To reconstruct chaotic signals from noisy observation data，an adaptive noise reduction method based on phase space reconstruction and singular spectrum analysis (SSA) is proposed． Due to the noiselike nature of chaos， it is difficult to identify the number of the singular values corresponding to the signal components when applying conventional SSA method to chaotic signals． To address this issue， the number of the singular values is estimated by comparing the statistical difference between the chaotic signals and the noise in the phase space． Accordingly， an adaptive noise reduction algorithm is designed． Noise reduction experiments corresponding to both chaotic signals generated by computer and the monthly mean sunspot number series are carried out． The results show that the proposed method can precisely estimate the number of the singular values of the signals，and effectively reconstruct the original chaotic signals． Compared with the conventional chaotic signal denoising methods， the proposed method has advantages in terms of both noise reduction performance and phase portrait restructuring quality．