ABSTRACTTwo species predator-prey with stage structure of mature and immature mathematical models are studied over the last few decades.Xin-an Zhang et alstudied a mathematical model with stage structure of two species in 2010. In this article, an attempt has been made to comprehend the coupled predator-prey dynamics with mature-immature stage structure and compare the dynamics with the existing model. The present model studied byXin-an Zhang et alis purely realistic with assumptions of positive parameters. From the mathematical curiosity, we wonder to investigate the same with complex parameters and compared with the foreseen results. In addition, the present model is slightly modified to see some new dynamics of some additional fixed point including the previous fixed points.