In this paper, the parameter identification problem for system of ordinary differential equations is considered. The parameter identification problem for system of ordinary differential equations is investigated by the Dzhumabaev’s parametrization method. At first, conditions for a unique solvability of the parameter identification problem for system of ordinary differential equations are obtained in the term of fundamental matrix of system’s differential part. Further, we establish conditions for a unique solvability of the parameter identification problem for system of ordinary differential equations in the terms of initial data. Algorithm for finding of approximate solution to a unique solvability of the parameter identification problem for system of ordinary differential equations is proposed and the conditions for its convergence are setted. Results this paper can be use for investigating of various problems with parameter and control problems for system of ordinary differential equations. The approach in this paper can be apply to the parameter identification problems for partial differential equations.