This paper deals with an identification problem which arises in adaptive control for partially known systems. The linear systems under consideration can be represented by a nonlinear parametric model which is polynomial in the unknown physical parameters, as opposed to the linear parametric model used in most black-box identification problem. A multilinear parametrization approach is proposed and an identification algorithm based on the multilinear model is developed. The properties of the multilinear identification algorithm are explored and analyzed. Simulation results are also presented to demonstrate the effectiveness of the proposed algorithm.