In this paper, we propose a deep learning (DL)-based parameter enhancement method for a mixed excitation linear prediction (MELP) speech codec in noisy communication environment. Unlike conventional speech enhancement modules that are designed to obtain clean speech signal by removing noise components before speech codec processing, the proposed method directly enhances codec parameters on either the encoder or decoder side. As the proposed method has been implemented by a small network without any additional processes required in conventional enhancement systems, e.g., time-frequency (T-F) analysis/synthesis modules, its computational complexity is very low. By enhancing the noise-corrupted codec parameters with the proposed DL framework, we achieved an enhancement system that is much simpler and faster than conventional T-F mask-based speech enhancement methods, while the quality of its performance remains similar.