Noise reduction is often essential for cochlear implant (CI) recipients to achieve acceptable speech perception in noisy environments. Most noise reduction algorithms applied to audio signals are based on time-frequency representations of the input, such as the Fourier transform. Algorithms based on other representations may also be able to provide comparable or improved speech perception and listening quality improvements. In this paper, a noise reduction algorithm for CI sound processing is proposed based on the wavelet transform. The algorithm uses a dual-tree complex discrete wavelet transform followed by shrinkage of the wavelet coefficients based on a statistical estimation of the variance of the noise. The proposed noise reduction algorithm was evaluated by comparing its performance to those of many existing wavelet-based algorithms. The speech transmission index (STI) of the proposed algorithm is significantly better than other tested algorithms for the speech-weighted noise of different levels of signal to noise ratio. The effectiveness of the proposed system was clinically evaluated with CI recipients. A significant improvement in speech perception of 1.9 dB was found on average in speech weighted noise.