The removal of mixed-noise is an ill-posed problem due to high level of non-linearity in the distribution of noise. Most commonly encountered mixed-noise is the combination of additive white Gaussian noise (AWGN) and impulse noise (IN) that have contrasting characteristics. A number of methods from the cascade of IN and AWGN reduction to the state-of-the-art sparse representation have been reported to reduce this common form of mixed-noise. In this paper, a new learning-based algorithm using the convolutional neural network (CNN) model is proposed to reduce the mixed Gaussian-impulse noise from images. The proposed CNN model learns the end-to-end mapping from noisy image to noise-free image. The model has a small structure yet is capable of providing superior performance as compared to the well established methods. Experimental results show that the proposed CNN-based denoising method performs better than the sparse representation and patch-based methods. Moreover, due to the lightweight structure, the denoising operation of the proposed CNN method is computationally faster than that of the established methods.