A new effective pair potential model is proposed for computer simulations of liquid methylene fluoride and used in Monte Carlo simulations on the isothermal-isobaric ensemble at two different temperatures. The new model is able to reproduce the thermodynamic (internal energy, density, heat capacity, vapor-liquid equilibrium) and structural (neutron diffraction data) properties of liquid methylene fluoride with good accuracy. The structure of liquid methylene fluoride is analyzed in detail on the basis of the present simulation at 153 K. It is found that, unlike in liquid water, the preferential location of the nearest neighbors is in the direction of the face centers of the tetrahedron of the central molecule. However, the four nearest neighbors do not surround the central molecule in a highly tetrahedral arrangement: the obtained distribution of the tetrahedral angular order parameter is rather similar to that in liquid argon. Preferential head-to-tail type orientation is found for nearest neighbors, accompanied by a slight preference for antiparallel dipole-dipole arrangement. The orientational correlation of the molecules is found to be rather long ranged, extending over the first coordination shell. The observed preferential nearest neighbor arrangement is resulted from the competition of steric and electrostatic interactions. No evidence for C-H ... F type hydrogen bonding is found in liquid methylene fluoride.