Nonlinear optical (NLO) effects in layered atomically thin two-dimensional (2D) materials provide a promising prospect for multifarious optoelectronic applications. The NLO characteristics of transition metal chalcogenides (TMDCs) are attracting growing attention and have been extensively explored recently. However, these materials possess sizable bandgaps ranging from visible to ultraviolet regions, so the investigation of narrow-bandgap materials remains deficient. Here, we report our comprehensive study on the NLO processes in palladium diselenide (PdSe2) flakes that have a near-infrared bandgap. Interestingly, this material exhibits a unique thickness-dependent second harmonic generation (SHG) feature, embodied in the strong (negligible) SHG signals in even (odd) layers, in contrast with that of other TMDCs. Furthermore, the two-photon absorption (TPA) coefficients (β ~4.5×105, 2.83×105, 1.7×105, and 1.85×104 cm/GW) of 1-3 L and bulk PdSe2 are larger by two and three orders of magnitude, compared with that of the conventional 2D materials. Significantly, at the excitation wavelength of 600 nm, a robust saturable absorption with giant modulation depths (αs ~47%, 30%, and 41%) was observed in 1-3 L PdSe2, which has yet been obtained in other 2D materials. Such unique NLO characteristics enable PdSe2 to be a potential candidate for technological innovations in nonlinear optoelectronic devices.