This paper addresses the problem of single-channel speech enhancement in the adverse environment. The critical-band rate scale based on improved multi-band spectral subtraction is investigated in this study for enhancement of single-channel speech. In this work, the whole speech spectrum is divided into different non-uniformly spaced frequency bands in accordance with the critical-band rate scale of the psycho-acoustic model and the spectral over-subtraction is carried-out separately in each band. In addition, for the estimation of the noise from each band, the adaptive noise estimation approach is used and does not require explicit speech silence detection. The noise is estimated and updated by adaptively smoothing the noisy signal power in each band. The smoothing parameter is controlled by a-posteriori signal-to-noise ratio (SNR). For the performance analysis of the proposed algorithm, the objective measures, such as, SNR, segmental SNR, and perceptual evaluations of the speech quality are conducted for the variety of noises at different levels of SNRs. The speech spectrogram and objective evaluations of the proposed algorithm are compared with other standard speech enhancement algorithms and proved that the musical structure of the remnant noise and background noise is better suppressed by the proposed algorithm.