Mesh-based Monte Carlo particle transport is suitable for complex geometry modeling and for multi-physics coupling calculations. Performing large-scale mesh-based Monte Carlo simulations requires a quite large amount of computation and memory space. Therefore, parallel Monte Carlo computing is crucial. In this study, a hybrid parallelism Monte Carlo transport middleware on mesh geometry was developed. The middleware can provide the following algorithms and functions: 1. hybrid parallelism of domain decomposition and particle parallelism; 2. particle data structure, which manages particle information and automatically performs asynchronous communication between decomposed domains; 3. subset data structure, which provides an efficient management strategy for materials and tally data; 4. particle tracking method on structured/unstructured mesh and k-dimensional tree (KD-Tree) acceleration algorithm; 5. condensed application programming interface for the rapid development of Monte Carlo code based on the middleware. We transplanted the fixed source module of the J Monte Carlo transport code (JMCT) which was based on constructive solid geometry (CSG) to the middleware for verification. The results indicated that the serial particle tracking efficiency of an unstructured mesh model was 6.56 times as high as that of MCNP6 and the serial simulation efficiency of the corresponding structured mesh model was basically equivalent to that of JMCT. The parallel efficiency of domain decomposition was higher than that of JMCT. We also calculated the shielding problem of the Qinshan No. 1 reactor through hybrid parallelism. The results were in good agreement with the experimental data, and the hybrid parallel efficiencies were higher than 65% on 4000 CPU cores.