High-fidelity life-cycle coupling simulations are attractive for increasing reactor power, increasing the fuel burnup and prolonging the reactor lifetime, which makes reactors much more economical. In this work, the continuous energy Reactor Monte Carlo code RMC was coupled to the subchannel code CTF. With the great support of the high-performance computing techniques, the coupled codes were then used to analyze VERA benchmark Problem 9 for the depletion of the fuel and burnable absorbers in a typical 18-month fuel cycle. Existing Monte Carlo burnup codes suffer from instabilities caused by spatial xenon oscillations. Therefore, a xenon equilibrium correction based on a simplified xenon-iodine burnup chain was used to restrain the spatial xenon oscillations and to improve simulation stability. The neutronics and thermal-hydraulics coupling convergence were investigated in terms of power distribution and Keff. The power distribution and Keff variations show that the neutronics/thermal-hydraulics coupling converges in the third iteration. To verify the neutronics/thermal-hydraulics coupling, the critical boron search algorithm and equilibrium xenon correction method, RMC/CTF solutions to a nominal flow and power critical calculation, VERA Benchmark Problem 7, were compared with the VERA reference solutions (MPACT/CTF) and MC21/CTF. The maximum relative difference of radial assembly power between this work and reference solutions was 2.8%. For the VERA Benchmark Problem 9, the measured critical boron concentrations were provided to validate coupling codes. The critical boron concentration prediction by RMC/CTF is consistent with the measured boron concentrations with absolute errors within 20 ppm, which is about 200 pcm in reactivity. The RMC/CTF solution for VERA Core Physics Benchmark Problem 9 is the first published coupled Monte Carlo neutronics/subchannel thermal-hydraulics solution for this problem.