This paper is concerned with the problem of suboptimal stable mixed H-2/H-infinity control for linear time-invariant systems. The designed controller with the same order as that of the considered system is required to satisfy a prescribed H-infinity performance bound or a prescribed degree of stability. By reducing the stable controller synthesis problem to a multi-objective state feedback control problem for two different state models, sufficient conditions for the solvability of the considered problem are given in terms of solutions to algebraic Riccati equations and matrix inequalities. An LMI-based iterative algorithm is developed to solve the stable controller synthesis problem. The proposed algorithm is shown to be convergent. Examples are given to illustrate the proposed methods.