This paper describes non-reference objective quality evaluation for noise-reduced speech. First, a subjective test is conducted in accordance with ITU-T Rec. P.835 to obtain the speech quality, the noise quality, and the overall quality of noise-reduced speech. Based on the results, we then propose an overall quality estimation model. The unique point of the proposed model is that the estimation of the overall quality is done only using the previously estimated speech quality and noise quality, in contrast to conventional models, which utilize the acoustical features extracted. Finally, we propose a non-reference objective quality evaluation method using the proposed model. The results of an experiment with different noise reduction algorithms and noise types confirmed that the proposed method gives more accurate estimates of the overall quality compared with the method described in ITU-T Rec. P.563.