This paper proposes a bound-based simulation budget allocation (BSBA) procedure for solving ranking and selection (R&S) problems in simulation optimization. For many practical applications, strict bounds on system performances can be obtained through empirical and theoretical approaches. These bounds provide additional information which may help solve R&S problems. In this paper, a new method of objective function estimation is proposed using both bound information and simulation outputs. This new estimation method is demonstrated to be particularly effective. To solve R&S problems, several asymptotic optimal allocation rules are also derived. Using these allocation rules, a BSBA procedure is proposed to achieve high efficiency in identifying the best design. Numerical experiments are provided to examine the performance of the proposed BSBA procedure. The computational results show that BSBA outperforms three compared allocation procedures, especially when bounds are tight or the simulation budget is small.