We study effect of magnetic field on massive dense core formation in colliding unequal molecular clouds by performing magnetohydrodynamic simulations with sub-parsec resolution (0.015 pc) that can resolve the molecular cores. Initial clouds with the typical gas density of the molecular clouds are immersed in various uniform magnetic fields. The turbulent magnetic fields in the clouds consistent with the observation by Crutcher et al. (2010) are generated by the internal turbulent gas motion before the collision, if the uniform magnetic field strength is 4.0 $mu$G. The collision speed of 10 km s$^{-1}$ is adopted, which is much larger than the sound speeds and the Alfv{e}n speeds of the clouds. We identify gas clumps with gas densities greater than 5 $times$ 10$^{-20}$ g cm$^{-3}$ as the dense cores and trace them throughout the simulations to investigate their mass evolution and gravitational boundness. We show that a greater number of massive, gravitationally bound cores are formed in the strong magnetic field (4.0 $mu$G) models than the weak magnetic field (0.1 $mu$G) models. This is partly because the strong magnetic field suppresses the spatial shifts of the shocked layer that should be caused by the nonlinear thin shell instability. The spatial shifts promote formation of low-mass dense cores in the weak magnetic field models. The strong magnetic fields also support low-mass dense cores against gravitational collapse. We show that the numbers of massive, gravitationally bound cores formed in the strong magnetic field models are much larger than the isolated, non-colliding cloud models, which are simulated for comparison. We discuss the implications of our numerical results on massive star formation.