Monte Carlo is one of the most common methods to solve radiation transport problems. However, due to its statistical nature, Monte Carlo is time-consuming when applied to large-scale problems. Therefore, parallel computing, a powerful tool in accelerating Monte Carlo calculations, has been receiving increasing attention along with new developments of computing hardware in recent years. This work documents the application of parallel computing in Geant4 simulations pertaining to nuclear logging tools. A user-specific interface is developed to enable Geant4 multithreading functionality for two nuclear logging models and the parallel Monte Carlo performance is evaluated on a designated HPC (high performance computing) platform. Upon the validation of the parallel-mode simulation, the performance of the Geant4-based simulation in multi-threaded mode (G4-MT) and with the G4-MPI native interface to MPI are compared to obtain the best combination of threads and processes on each node. Strong and weak scalabilities on multiple threads are then investigated by computing the speedup and the parallel efficiency of the simulation. The results show that combining multi-threaded and MPI-based execution can significantly reduce execution time in parallel mode. And the paper documents the improvement of Monte Carlo simulation efficiency by optimizing the configuration of computational resources for parallel execution while keeping close-to-linear acceleration.