Class activation mapping (CAM) interprets the decision-making process of deep learning models by generating saliency maps. However, existing CAM methods often encounter difficulties in simultaneously achieving both high precision and robustness. A multi-step gradient class activation mapping (MG-CAM) method is presented, which is built upon a multi-step gradient optimization framework. The approach enhances the precision and reliability of saliency map representation by introducing a multi-step gradient optimization strategy, integrating multi-dimensional feature information, and dynamically adjusting the weight distribution across feature maps. Experiments on the ImageNet dataset demonstrate that MG-CAM achieves satisfactory performance across various evaluation metrics. Additionally, robustness checks and ablation studies have been conducted on MG-CAM, which validate its sensitivity to model parameters and the effectiveness of the multi-gradient optimization strategy. A potential direction is provided for improving the interpretability of deep learning models.