Abstract: We consider to identify the parameters.which are functions of spatial and or time variables,in a quasi-linear parabolic equation.First,we prove that the solution of the parabolic equation is a smooth function with respect to the parameters,and then we give a modified Newton-Kantorovich iteration regularity method(NKR) to construct the solution of the inverse problem of the partial differential equation.Secondly,we give a proof of convergence for NKR. Finally,we give a computational example to show that the sequence generated by NKR does converge to the real solution of the inverse problem when the initial guess is close to it.