Simulation studies have been essential for development of SPECT imaging systems. GATE is one of the most commonly used simulation toolkits in nuclear medicine. This software package allows the users to build system geometries and phantoms based on primitive objects such as cylinder, sphere, and cube. However, modeling systems with complex geometry is challenging, if not impossible using these primitive volumes. The latest GATE release addressed this issue by allowing the users to import surface meshes created in a computer aided design software thus enabling accurate simulation of complex system or phantom geometries. In this study we present our GATE mesh-based simulations of a next-generation multi-pinhole SPECT system for the clinical brain imaging, called AdaptiSPECT-C. An additional challenge with the AdaptiSPECT-C is that the volume of the standard voxelized XCAT phantom overlaps with the spherical collimator plate. In order to address this issue, we developed a mesh modeling of the XCAT human phantom by directly using the native XCAT nurbs data, which also provided a more accurate representation of the anatomy. Two approaches for simulating mesh-based activity source were developed and evaluated. The first method consisted of using an acceptance/rejection criterion confining a cubical source into the mesh object and the second one was based on a conversion of a mesh-based volume into a voxelized object. Although the two strategies led to very similar results, the voxelized-mesh approach was significantly faster in computation time. We successfully imported and simulated in GATE a complete SPECT acquisition incorporating an STL representation of system, phantom anatomy, and activity source.