Speech understanding in noisy environments is still one of the major challenges for cochlear implant (CI) users in everyday life. We evaluated a speech enhancement algorithm based on neural networks (NNSE) for improving speech intelligibility in noise for CI users. The algorithm decomposes the noisy speech signal into time-frequency units, extracts a set of auditory-inspired features and feeds them to the neural network to produce an estimation of which frequency channels contain more perceptually important information (higher signal-to-noise ratio, SNR). This estimate is used to attenuate noise-dominated and retain speech-dominated CI channels for electrical stimulation, as in traditional n-of-m CI coding strategies. The proposed algorithm was evaluated by measuring the speech-in-noise performance of 14 CI users using three types of background noise. Two NNSE algorithms were compared: a speaker-dependent algorithm, that was trained on the target speaker used for testing, and a speaker-independent algorithm, that was trained on different speakers. Significant improvements in the intelligibility of speech in stationary and fluctuating noises were found relative to the unprocessed condition for the speaker-dependent algorithm in all noise types and for the speaker-independent algorithm in 2 out of 3 noise types. The NNSE algorithms used noise-specific neural networks that generalized to novel segments of the same noise type and worked over a range of SNRs. The proposed algorithm has the potential to improve the intelligibility of speech in noise for CI users while meeting the requirements of low computational complexity and processing delay for application in CI devices.