Dynamic objects diversify the distribution of point cloud in the map, degrading the performance of the robotic downstream tasks. To address this problem, we present a novel real-time dynamic instance-aware static mapping framework called DynaInsRemover, which exploits the geometric discrepancies between instances to efficiently remove dynamic objects and preserve more details of static map. It contains the Instance Occupancy Check module for initial dynamic instance proposal and the Instance Belief Update module for reverting false positives. We quantitatively evaluate our approach performance on the SemanticKITTI dataset and validate it in a real-world environment. Experimental evaluations show that our method achieves very promising results in dynamic environments. The implementation of our method is available as open source at: https://github.com/Zhaohuanfeng/DynaInsRemover.git.