Abstract: A hierarchical optimization method for the identification of LTI state-space systems is proposed based on projected gradient search. The system parameters are determined by optimizing an output-error cost function. To deal with the non-uniqueness of the fully parameterized state-space system, a projected gradient search algorithm is presented by restricting the update of the parameters to the tangent space to the manifold of observationally equivalent state-space systems. The sufficient condition to employ L-M algorithm for optimizing parameters is also introduced. The proposed hierarchical optimization identificationmethod includes two steps: First, the parameter search direction is determined by the proposed adaptive L-M projected gradient approach; Second, the optimum step size is computed according to a line search method. Numerical simulation studies show that the proposed algorithm offers improved performance, such as faster convergence speed and better numerical stability, over existing EM and DDLCmethods.