To reveal the origins of diffuse H-alpha emissions observed around the Herbig star MWC 1080, we have performed a high-resolution near-infrared (NIR) spectroscopic observation using the Immersion GRating INfrared Spectrograph (IGRINS). In the NIR H and K bands, we detected various emission lines (six hydrogen Brackett lines, seven H2 lines, and an [Fe II] line) and compared their spatial locations with the optical (H-alpha and [S II]) and radio (13CO and CS) line maps. The shock-induced H2 and [Fe II] lines indicate the presence of multiple outflows, consisting of at least three, associated young stars in this region. The kinematics of H2 and [Fe II] near the northeast (NE) cavity edge supports that the NE main outflow from MWC 1080A is the blueshifted one with a low inclination angle. The H2 and [Fe II] lines near the southeast molecular region newly reveal that additional highly-blueshifted outflows originate from other young stars. The fluorescent H2 lines were found to trace photodissociation regions formed on the cylindrical surfaces of the main outflow cavity, which are expanding outward with a velocity of about 10-15 km/s. For the H-alpha emission, we identify its components associated with two stellar outflows and two young stars in addition to the dominant component of MWC 1080A scattered by dust. We also report a few faint H-alpha features located ~0.4 pc away in the southwest direction from MWC 1080A, which lie near the axes of the NE main outflow and one of the newly-identified outflows.