Grand canonical Monte Carlo (GCMC) simulations have been conducted to investigate freezing phenomena of Lennard-Jones (LJ) methane confined in cylindrical nanopores of reduced pore diameter ranging from 4.5 to 9.5 with saturated vapor as equilibrium bulk condition. The arrangement of the LJ particles in frozen state is found to form a hexagonal array within each concentric circular layer. Nonmonotonic dependence of freezing point against pore diameter, which is observed in strongly attractive pore made of carbon, is interpreted as a result of competition between "geometrical hindrance effect" of a wall's shape and "compression effect" of a wall's attractive potential. Geometrical hindrance effect, which originates from excess energy of "cylindrical frozen state" relative to the fee lattice state,;is clarified to become stronger for smaller pore size. The latent heat is also smaller for smaller pore size. We model the shift of freezing point in cylindrical pore considering the "geometrical hindrance effect," and its reliability is verified successfully through comparison with the GCMC results.