A handful of computational benchmarks that incorporate VVER-1000 assemblies having low enriched uranium (LEU) and the mixed oxide (MOX) fuel have been put forward by many experts across the world from the Nuclear Energy Agency. To study & scrutinize the characteristics of one of the VVER-1000 LEU & MOX assembly benchmarks in different states were considered. In this work, the VVER-1000 LEU and MOX Assembly computational-benchmark exercises are performed using the OpenMC software. The work was intended to test the preciseness of the OpenMC Monte Carlo code using nuclear data library ENDF/B-VII.1, against a handful of previously obtained solutions with other computer codes. The kinf value obtained was compared with the SERPENT and MCNP result, which presented a very good similarity with very few deviations. The kinf variation with respect to burnup upto 40 MWd/kgHM was obtained for State-5 by using OpenMC code for both the LEU and MOX fuel assembly. The depletion curves of isotope concentrations against burnup upto 40 MWd/kg/HM were also generated for both the LEU and MOX fuel assembly. The OpenMC results are comparable with those of benchmark mean values. The neutron energy vs flux spectrum was also generated by using OpenMC code. Based on the OpenMC results such as kinf, burnup, isotope concentrations and neutron energy spectrum, it is concluded that the OPenMC code with ENDF/B-VII.1 nuclear data library was successfully implemented. It is planned to use OpenMC code for calculation of neutronics and burnup of the VVER-1200 reactor to be commissioned in Bangladesh by 2023/2024.