Abstract: This paper presents a two-step algorithm for the worst case H~ identification of a class of well-known model set with time domain experimental data. Using the information consistency principle, the first step of the algorithm transforms the identification problem into a constrained convex programming ,the result of which is then used ,in the second step, to approximate systems in the uncertainty set to obtain the identified nominal model based on a polynomial approximation theorem. Discussions on the local and global identification errors and the convergence of the algorithm are also carried out respectively.