The realm of Weakly Supervised Instance Segmentation (WSIS) under box supervision has garnered substantial attention, showcasing remarkable advancements in recent years. However, the limitations of box supervision become apparent in its inability to furnish effective information for distinguishing foreground from background within the specified target box. This research addresses this challenge by introducing pseudo-depth maps into the training process of the instance segmentation network, thereby boosting its performance by capturing depth differences between instances. These pseudo-depth maps are generated using a readily available depth predictor and are not necessary during the inference stage. To enable the network to discern depth features when predicting masks, we integrate a depth prediction layer into the mask prediction head. This innovative approach empowers the network to simultaneously predict masks and depth, enhancing its ability to capture nuanced depth-related information during the instance segmentation process. We further utilize the mask generated in the training process as supervision to distinguish the foreground from the background. When selecting the best mask for each box through the Hungarian algorithm, we use depth consistency as one calculation cost item. The proposed method achieves significant improvements on Cityscapes and COCO dataset.