In a real options and game-theoretic framework, this paper examines the optimal R&D investment timing of an incumbent under uncertainty, which faces the threat of preemption by a potential entrant. We incorporate incomplete information into the model by assuming that the incumbent does not know the entrant’s investment timing but know its distribution. We find that incomplete information reduces the erosion of waiting option value by the competition, and therefore waiting is still valuable even in the presence of preemption and competition. The entrant's hazard rate has the impact on the incumbent's optimal investment timing: the more the hazard rate is, the earlier the incumbent invests.