The real symmetric matrix is widely applied in various fields, transforming non-symmetric matrix to symmetric matrix becomes very important for solving the problems associated with the original matrix. In this paper, we consider the constrained inverse eigenvalue problem for symmetrizable matrices, and obtain the solvability conditions and the general expression of the solutions. Moreover, we consider the corresponding optimal approximation problem, obtain the explicit expressions of the optimal approxima- tion solution and the minimum norm solution, and give the algorithm and corresponding computational example