This paper presents a haptics-based training simulator for dental implant surgery. Most of the previously developed dental simulators are targeted for exploring and drilling purpose only. The penalty-based contact force models with spherical-shaped dental tools are often adopted for simplicity and computational efficiency. In contrast, our simulator is equipped with a more precise force model adapted from the Voxmap-PointShell (VPS) method to capture the essential features of the drilling procedure, with no limitations on drill shape. In addition, a real-time torque model is proposed to simulate the torque resistance in the implant insertion procedure, based on patient-specific tissue properties and implant geometry. To achieve better anatomical accuracy, our oral model is reconstructed from cone beam computed tomography (CBCT) images with a voxel-based method. To enhance the real-time response, the parallel computing power of GPUs is exploited through extra efforts in data structure design, algorithms parallelization, and graphic memory utilization. Results show that the developed system can produce appropriate force feedback at different tissue layers during pilot drilling and can create proper resistance torque responses during implant insertion.