In this study, a single microphone speech enhancement algorithm is proposed to improve speech intelligibility for cochlear implant recipients. The proposed algorithm combines harmonic structure estimation with a subsequent statistical based speech enhancement stage. Traditional minimum mean square error (MMSE) based speech enhancement methods typically focus on statistical characteristics of the noise and track the noise variance along time dimension. The MMSE method is usually effective for stationary noise, but not as useful for non-stationary noise. To address both stationary and non-stationary noise, the current proposed method not only tracks noise over time, but also estimates the noise structure along the frequency dimension by exploiting the harmonic structure of the target speech. Next, the estimated noise is employed in the traditional MMSE framework for speech enhancement. To evaluate the proposed speech enhancement solution, a formal listener evaluation was performed with 6 cochlear implant recipients. The results suggest that a substantial improvement in speech intelligibility performance can be gained for cochlear implant recipients in noisy environments.