Noise removal is a classic problem. Most researchers focus on Gaussian noise removal due to the regularity of the noise distribution, while mixed noise removal is always challenging because of the uncertainty of the noise distribution. Mixtures of additive white Gaussian noise (AWGN) with salt-and-pepper impulse noise (SPIN) and mixtures of AWGN with random-valued impulse noise (RVIN) are typical examples of mixed noise. Most mixed noise removal methods are effective in the removal of mixed AWGN and SPIN, but perform poorly in the removal of AWGN and RVIN. The main reason is the randomness of RVIN, which leads to poor denoising performance when the RVIN is strong. In this paper, an improved nonlocal means-based correction strategy (INS) is proposed. In INS, an improved nonlocal means strategy is applied to replace the impulse noise pixels to make the mixed noise obey an approximate Gaussian distribution. To prove the validity of INS, a convolutional neural network (CNN) in combination with INS (CNNINS) is applied to remove mixed noise. Experimental results are used to compare the proposed CNNINS with the most advanced mixed noise removal methods.