Utilizing a human-perception-related objective function to train a speech enhancement model has become a popular topic recently. The main reason is that the conventional mean squared error (MSE) loss cannot represent auditory perception well. One of the typical hu-man-perception-related metrics, which is the perceptual evaluation of speech quality (PESQ), has been proven to provide a high correlation to the quality scores rated by humans. Owing to its complex and non-differentiable properties, however, the PESQ function may not be used to optimize speech enhancement models directly. In this study, we propose optimizing the enhancement model with an approximated PESQ function, which is differentiable and learned from the training data. The experimental results show that the learned surrogate function can guide the enhancement model to further boost the PESQ score (in-crease of 0.18 points compared to the results trained with MSE loss) and maintain the speech intelligibility.