We present the results of analyses of the 12CO (J=1-0), 13CO (J=1-0), and 12CO (J=2-1) emission data toward Gum 31. Three molecular clouds separated in velocity were detected at -25, -20, and -10 km/s . The velocity structure of the molecular clouds in Gum 31 cannot be interpreted as expanding motion. Two of them, the -25 km/s cloud and the -20 km/s cloud, are likely associated with Gum 31, because their 12CO (J=2-1)/12CO (J=1-0) intensity ratios are high. We found that these two clouds show the observational signatures of cloud-cloud collisions (CCCs): a complementary spatial distribution and a V-shaped structure (bridge features) in the position-velocity diagram. In addition, their morphology and velocity structures are very similar to the numerical simulations conducted by the previous studies. We propose a scenario that the -25 km/s cloud and the -20 km/s cloud were collided and triggered the formation of the massive star system HD 92206 in Gum 31. This scenario can explain the offset of the stars from the center and the morphology of Gum 31 simultaneously. The timescale of the collision was estimated to be ~1 Myr by using the ratio between the path length of the collision and the assumed velocity separation. This is consistent with that of the CCCs in Carina Nebula Complex in our previous study.