We report the discovery of a sub-Jovian-mass planet, OGLE-2014-BLG-0319Lb. The characteristics of this planet will be added into a future extended statistical analysis of the Microlensing Observations in Astrophysics (MOA) collaboration. The planetary anomaly of the light curve is characterized by MOA and OGLE survey observations and results in three degenerate models with different planetary-mass ratios of q = (10.3, 6.6, 4.5) × 10-4. We find that the last two models require unreasonably small lens-source relative proper motions of μ rel ~ 1 mas yr-1. Considering Galactic prior probabilities, we rule out these two models from the final result. We conduct a Bayesian analysis to estimate physical properties of the lens system using a Galactic model and find that the lens system is composed of a ${0.49}_{-0.27}^{+0.35}\ {M}_{\mathrm{Jup}}$ sub-Jovian planet orbiting a ${0.47}_{-0.25}^{+0.33}\ {M}_{\odot }$ M dwarf near the Galactic Bulge. This analysis demonstrates that Galactic priors are useful to resolve this type of model degeneracy. This is important for estimating the mass-ratio function statistically. However, this method would be unlikely successful in shorter timescale events, which are mostly due to low-mass objects, like brown dwarfs or free-floating planets. Therefore, careful treatment is needed for estimating the mass-ratio function of the companions around such low-mass hosts, which only the microlensing can probe.