We present a theoretical study of the nonlinear dynamics of a long external cavity delayed optical feedback-induced interband cascade laser (ICL). Using the modified Lang–Kobayashi equations, we numerically investigate the effects of some key parameters on the first Hopf bifurcation point of ICL with optical feedback, such as the delay time (τf), pump current (I), linewidth enhancement factor (LEF), stage number (m) and feedback strength (fext). It is found that compared with τf, I, LEF and m have a significant effect on the stability of the ICL. Additionally, our results show that an ICL with few stage numbers subjected to external cavity optical feedback is more susceptible to exhibiting chaos. The chaos bandwidth dependences on m, I and fext are investigated, and 8 GHz bandwidth mid-infrared chaos is observed.