Additive noise degrades speech quality and intelligibility. Speech enhancement reduces this noise to make speech more pleasant and intelligible. It plays a significant role in speech recognition or speech-operated systems. In this paper, we propose a single-channel speech enhancement method in which the log-minimum mean square error method (log-MMSE) and modified accelerated particle swarm optimization algorithm are used to design a filter for improving the quality and intelligibility of noisy speech. Accelerated particle swarm optimization (APSO) algorithm is modified in which a single dimension of particle position is changed in a single iteration while obtaining the particle's new position. Using this algorithm, a filter is designed with multiple passbands and notches for speech enhancement. The modified algorithm converges faster compared with standard particle swarm optimization algorithm (PSO) and APSO giving optimum filter coefficients. The designed filter is used to enhance the speech. The proposed speech enhancement method improves the perceptual estimation of speech quality (PESQ) by 17.05% for 5dB babble noise, 33.92 % for 5dB car noise, 14.96 % for 5dB airport noise, and 39.13 % for 5dB exhibition noise. The average output PESQ for these four types of noise is improved compared to conventional methods of speech enhancement. There is an average of 7.58 dB improvement in segmental SNR for these noise types. The proposed method improves speech intelligibility with minimum speech distortion. © 2022 Penerbit UTM Press. All rights reserved.