In this work, bifurcation and a systematic approach for estimation of identifiable parameters of a modified Leslie–Gower predator-prey system with Crowley–Martin functional response and prey refuge is discussed. Global asymptotic stability is discussed by applying fluctuation lemma. The system undergoes into Hopf bifurcation with respect to parameters intrinsic growth rate of predators (s) and prey reserve (m). The stability of Hopf bifurcation is also discussed by calculating Lyapunov number. The sensitivity analysis of the considered model system with respect to all variables is performed which also supports our theoretical study. To estimate the unknown parameter from the data, an optimization procedure (pseudo-random search algorithm) is adopted. System responses and phase plots for estimated parameters are also compared with true noise free data. It is found that the system dynamics with true set of parametric values is similar to the estimated parametric values. Numerical simulations are presented to substantiate the analytical findings. © 2017 Elsevier B.V.