A real-time multi-step planning problem is characterized by alternating decision-making and execution processes, whole online decision-making time divided in slices between each execution, and the pressing need for policy that only relates to current step. We propose a new criterion to judge the optimality of a policy based on the upper and lower bound theory. This criterion guarantees that the agent can act earlier in a real-time decision process while an optimal policy with sufficient precision still remains. We prove that, under certain conditions, one can obtain an optimal policy with arbitrary precision using such an incremental method. We present a Bounded Incremental Real-Time Dynamic Programming algorithm (BIRTDP). In the experiments of two typical real-time simulation systems, BIRTDP outperforms the other state-of-the-art RTDP algorithms tested.