Abstract: The method of characteristics (MOC) has gained significant attention in high-fidelity neutron transport calculations for reactor cores due to its geometric flexibility, high accuracy, and inherent parallelizability. However, its direct application to three-dimensional (3D) core transport calculations faces challenges such as excessive memory requirements and computational costs. While the widely adopted 2D/1D coupling method resolves these issues by decomposing the problem into radial 2D MOC and axial 1D calculations, it suffers from reduced geometric flexibility, numerical instabilities in axially heterogeneous systems, and axial mesh mismatches during control rod movements. To address these limitations, the random ray method (TRRM) was proposed, which dynamically generates rays and uniformly samples the starting points and directions of each ray. This method eliminates the need for storing ray information and reduces ray density required by deterministic MOC. Despite its advantages, TRRM suffers from slow convergence due to the statistical variance inherent in random sampling, with a convergence rate of O(N^−1/2). This study preliminarily developed a 3D neutron transport calculation code based on TRRM and applies it to the 3D C5G7 benchmark calculation. Firstly, a sensitivity analysis of ray parameters, including the number of rays, the tracking distance, and the length of dead zone, was performed to determine optimal calculation configuration. Secondly, three core configurations of the 3D C5G7 benchmark were calculated by TRRM, and key parameters, including the effective multiplication factor (k_eff), pin power distributions, and axial power profiles, were compared with multi-group Monte Carlo (MGMC) to validate accuracy. Finally, a quasi-random variant of TRRM (QRRM) was tested, where low-discrepancy sequences replaced uniform random sampling to improve convergence. Numerical results demonstrate that TRRM achieves excellent agreement with Monte Carlo calculations, where the maximum deviation in k_eff is within 20 pcm, the averaged pin power relative deviation is below 0.2%, and the maximum pin power relative deviation is within 1%. In addition, the relative deviations of axial power profiles are less than 0.1%. QRRM significantly accelerates the convergence of k_eff, reducing the required number of active batches from 228 (TRRM) to 27 to achieve a standard deviation of 10 pcm. However, QRRM exhibits no notable improvement in pin power convergence, likely because the rays need to traverse a certain distance in the core and reduces the advantages of low-discrepancy sequences. Future efforts should focus on coupling TRRM with coarse-mesh finite difference (CMFD) method during active batches to provide a stabilized fission source distributions and enhance convergence rates for localized quantities such as pin power. This study validates the accuracy of the TRRM in three-dimensional transport calculations. The sensitivity analysis of ray parameters and the application of quasi-random numbers provide an effective approach for further optimizing TRRM computations.