This paper presents the clinical results of the application of a deep-learning-based noise reduction (NR) approach to improve speech intelligibility for cochlear implant (CI) recipients in the presence of competing speech noise. The deep denoising autoencoder (DDAE) model was used as a representative deep-learning-based NR model to reduce the noise components from the noisy input. The enhanced speech was subsequently played to six Mandarin-speaking CI recipients to perform recognition tests. All the subjects used their own clinical speech processors during testing. Two traditional NR approaches were also implemented to test the performance for a comparison. The Taiwan Mandarin version of the hearing in noise test (TMHINT) sentences were adopted and further corrupted by competing two talker speech noise at signal-to-noise ratio (SNR) levels of 0 and 5 dB. The experimental results showed that the DDAE NR approach can yield higher intelligibility scores than the two classical NR techniques in the presence of competing speech. The results of qualitative analysis further showed that the DDAE NR approach notably reduced the envelope distortions. The good results also suggest that the proposed DDAE NR approach can combine well with the existing CI processors to overcome the issue of degradation of speech perception, which is caused by competing speech noise.