The broadband nonlinear optical material towards the mid-infrared spectral range is highly needed for civil and military applications. Here, we have investigated the nonlinear optical response of the nickel ditelluride (NiTe_2) single crystal prepared by the chemical vapor deposition (CVD) method, and found that the layered NiTe_2 exhibits attractive broadband nonlinear optical absorption performance towards the mid-infrared regime. We further explored the nonlinear optical response of the layered NiTe_2 in the erbium-doped fluoride fiber laser, and have realized the stable Q-switched fiber laser with a pulse width of 708 ns and a repetition rate of 81 kHz around 2.8 µm wavelength. The experimental results may not only make inroads towards the understanding the nonlinear optical response of the topological materials, but also explore their broadband applications in mid-infrared photonics.