In this paper, we report a high-sensitive extended short-wave infrared (e-SWIR) Electron-Injection (EI) photodetector based on InGaAs/GaAsSb type-II superlattice (T2SL). To achieve high gain and low dark current noise, the EI photodetector involved in this letter employs a multi-layer heterogeneous band structure, composed of InAlAs, GaAsSb and InGaAs/GaAsSb T2SL, which can facilitate electron injection and effectively reduce recombination and thermal generation within the device. Thanks to the unique band alignment, this EI photodetector operates in high-gain linear-mode and requires only a small bias voltage about 0.8 V. At 200 K, the detector exhibits a 100 % cut-off wavelength of similar to 2.7 mu m, a peak responsivity of 3693.2 A/W corresponding to a gain of 7979.0 at 1.4 V, and a gain-normalized dark current density (GNDCD) of 1.4 x 10(-6) A/cm(2), which results in a remarkable specific detectivity of 6.0 x 10(13) cm<middle dot>Hz(1/2)/W. When operating at room temperature, this EI photodetector presents a decent responsivity of over 2000.0 A/W. Our results pave a potential way for ultra-sensitive e-SWIR infrared detection at high temperature.