The present paper describes the coupling of a three-dimensional continuous-energy Monte Carlo reactor physics code, Serpent, with thermal-hydraulics safety analysis code RELAP5. Thermal-hydraulics and reactor physics coupling is commonly used in deterministic methods, for example RELAP5/PARCS and TRACE/PARCS. It has been well-validated for a number of steady and transient problems. The coupling of Monte-Carlo and reactor thermal-hydraulics will significantly improve the MC predictive capability and its applicability to a wide range of reactor problems of practical interest, as right now it is limited to fixed-feedback conditions. In this paper, the coupled Serpent/RELAP5 code capability is demonstrated by the improved axial power distribution of UO2 and MOX single assembly models, based on the OECD-NEA/NRC PWR MOX-UO2 Core Transient Benchmark1. Comparisons of calculation results using the coupled code with those from the deterministic methods, specifically heterogeneous multi-group transport code DeCART, show that the coupling produces more precise results. In addition, a new convergence criterion based on the normalized axial power distribution is introduced, which is proved to be more direct, easier to apply and more rigorous than the temperature convergence used in previous research.