Generative Adversarial Networks (GANs) have achieved remarkable success in image translation tasks. However, its prohibitive computational overhead has been a major hurdle for deployment on resource constrained platforms. Due to the training instability and the complicated network architecture, existing model acceleration techniques cannot appropriately handle the GAN compression problem. To cope with these difficulties, we propose a multi-objective evolutionary algorithm to compress GAN models in the context of image translation tasks, which is termed as MEGC. Particularly, the conflict between the computational cost of the GAN model and the quality of generated image is explicitly modeled as a two-objective optimization problem, and the evolved Pareto set is utilized to guide the sampling process during supernet training, which can in turn divert the focus of the supernet training to well-performing compact subnets. Besides, an evaluation-free strategy is introduced to facilitate exploration in the search space while incurring no extra computational cost. Based on the above design, the proposed MEGC eliminates the requirement of subnet searching in the post-processing procedure. Experiments on image translation tasks under paired and unparied settings demonstrate the effectiveness of the proposed MEGC on reducing the computational cost of GANs while improving the quality of generated images compared to those of the full models.