Electrical noise significantly limits the detectivity of infrared photodiode detectors. In this paper, we investigated the dark current and noise spectra for long-wave-infrared InAs/GaSb type-II superlattice (T2SL) detectors to study the origin of noise under various work conditions. The temperature-dependent I-V characteristics reveal a turning point near 90 K, below which the dominant dark current mechanism changes from Shockley-Hall-Read generation current and diffusion current to shunt current and trap-assisted tunneling (TAT) current. The contribution of shunt and tunneling process to the total 1/f noise are analyzed by fitting the noise power spectral density at 77 K for detectors. It is found that the TAT current dominates the 1/f noise at the reverse bias stronger than -0.1 V, while shunt current exhibits a larger contribution at the reverse bias less than -0.1 V with the shunt noise coefficient αshunt of 5×10-8. Furthermore, the leakage routes related to the shunt process and their temperature dependence are illustrated by two-dimensional photocurrent mapping.