Nonlinear effects in two-dimensional (2D) atomic layered materials have recently attracted increasing interest. Phenomena such as nonlinear optical edge response, chiral electroluminescence, and valley and spin currents beyond linear orders have opened up a great opportunity to expand the functionalities and potential applications of 2D materials. Here we report the first observation of strong optical second-harmonic generation (SHG) in monolayer GaSe under nonresonant excitation and emission condition. Our experiments show that the nonresonant SHG intensity of GaSe is the strongest among all the 2D atomic crystals measured up to day. At the excitation wavelength of 1600 nm, the SHG signal from monolayer GaSe is around 1-2 orders of magnitude larger than that from monolayer MoS2 under the same excitation power. Such a strong nonlinear signal facilitates the use of polarization-dependent SHG intensity and SHG mapping to investigate the symmetry properties of this material: the monolayer GaSe shows 3-fold lattice symmetry with an intrinsic correspondence to its geometric triangular shape in our growth condition; whereas the bilayer GaSe exhibits two dominant stacking orders: AA and AB stacking. The correlation between the stacking orders and the interlayer twist angles in GaSe bilayer indicates that different triangular GaSe atomic layers have the same dominant edge configuration. Our results provide a route toward exploring the structural information and the possibility to observe other nonlinear effects in GaSe atomic layers.