Mega-constellation networks have recently gained significant research attention because of their potential for providing ubiquitous and high-capacity connectivity in future sixth-generation (6G) wireless communication systems. However, the high dynamics of network topology and large-scale of a mega-constellation pose new challenges to constellation simulation and performance evaluation. To address these issues, we introduce UltraStar, a high-fidelity and high-efficiency computer simulator to support the development of 6G wireless communication systems with low-Earth-orbit mega-constellation satellites. The simulator facilitates the design and performance analysis of various algorithms and protocols for network operation and deployment. We propose a systematic, scalable, and comprehensive simulation architecture for the high-fidelity modeling of network configurations and for performing high-efficiency simulations of network operations and management capabilities, while providing users with intuitive visualizations. We capture heterogeneous topology characteristics by establishing an environment update algorithm that incorporates real ephemeris data for satellite orbit prediction, sun outages, and link handovers. For a realistic simulation of software and hardware configurations, we develop a network simulator version 3 based network model to support networking protocol extensions. We propose a message passing interface-based parallel and distributed approach with multiple cores or machines to achieve high simulation efficiency in large and complex network scenarios. Experimental results demonstrate the high fidelity and efficiency of UltraStar can help pave the way for 6G integrated space-ground networks.