A recently synchronized Janus TMD material with broken out-of-plane symmetry offers a vertical dipole to enhance nonlinear optical behavior. Here, by comparing the second harmonic generation properties of MoS2 and MoSSe monolayers, we investigated the nonzero out-of-plane SHG susceptibilities of a Janus MoSSe 2D material. A three-fold enhancement of out-of-plane SHG susceptibilities exists in three stacked bulks of Janus MoSSe compared to that in the monolayer. A sensitivity to their stack pattern is also found. The broken out-of-plane symmetry, vertical dipole, and intrinsic tunable electronic properties of Janus two-dimensional materials make MoSSe a promising nanomaterial for nonlinear optical devices.