This paper proposes a multi-band speech enhancement algorithm exploiting iterative processing for enhancement of single channel speech. In the proposed algorithm, the output of the multi-band spectral subtraction (MBSS) algorithm is used as the input signal again for next iteration process. As after the first MBSS processing step, the additive noise transforms to the remnant noise, the remnant noise needs to be further re-estimated. The proposed algorithm reduces the remnant musical noise further by iterating the enhanced output signal to the input again and performing the operation repeatedly. The newly estimated remnant noise is further used to process the next MBSS step. This procedure is iterated a small number of times. The proposed algorithm estimates noise in each iteration and spectral over-subtraction is executed independently in each band. The experiments are conducted for various types of noises. The performance of the proposed enhancement algorithm is evaluated for various types of noises at different level of SNRs using, 1) objective quality measures: signal-to-noise ratio (SNR), segmental SNR, perceptual evaluation of speech quality (PESQ); and 2) subjective quality measure: mean opinion score (MOS). The results of proposed enhancement algorithm are compared with the popular MBSS algorithm. Experimental results as well as the objective and subjective quality measurement test results confirm that the enhanced speech obtained from the proposed algorithm is more pleasant to listeners than speech enhanced by classical MBSS algorithm.