Dark current and responsivity are two important parameters of quantum well infrared photodetectors (QWIPs). An optimization approach is applied herein to achieve low dark current along with high responsivity for a GeSn/SiGeSn QWIP. The dark current is reduced by varying different physical parameters of well and barrier, operating temperature and bias voltage of the QWIP. To optimize the QWIP, the detectivity is calculated. The results show that the optimally designed GeSn/SiGeSn QWIP can achieve a low dark current of 2.35 pA at 2 V with a peak responsivity of 1.24 A/W at 4.3 µm and a high detectivity of 3.47 × 1012 cm · Hz1/2 W−1 at 2 V and 77 K. Finally, the frequency response of the optimally designed GeSn/SiGeSn QWIP device is estimated. The theoretically predicted higher detectivity with respect to previously reported SiGe/Si QWIPs and GeSn/SiGeSn interband QWIPs indicates a promising future for GeSn/SiGeSn intersubband QWIPs. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.