This paper considers competitive project scheduling on two unbounded parallel batch machines. There are two competing firms, and each firm has an unbounded parallel batch machine. All projects must be performed in batches by Firms 1 and 2 on their machines, respectively. The profit that each firm obtains from each project depends on whether the firm finishes the job before or after its competitor. In the first problem, given a feasible schedule for Firm 1, the objective is to find an optimal schedule to maximize the total reward for Firm 2 under the given schedule for Firm 1. The corresponding total reward for Firm 1 is called the worst-case total reward of the given schedule for Firm 1. In the second problem, the objective is to find an optimal schedule for Firm 1 to maximize the worst-case total reward. We provide optimal algorithms for the two problems, respectively.