A generic numerical model of a long-wavelength Avalanche Photodiode (APD) based on narrow bandgap semiconductor InAsSb on InAs substrate is reported for the first time. This model has been applied for theoretical characterization of a proposed N InAS/P-InAsSb avalanche photodiode structure for possible application in 2-5 μm wavelength region. The parameters such as gain,excess noise factor and their trade-off with variation of doping concentration and bias voltage have been estimated for the APD taking into account history-dependent theory of avalanche multiplication process. The LWIR APD is expected to find application in optical gas sensor and in future generation of optical communication system.