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With the increase in cloud users and internet of things (IoT) applications, advanced task scheduling (TS) methods are required to reasonably schedule tasks in cloud computing. This study proposes a diversity-aware marine predators algorithm (DAMPA) for solving TS in cloud computing. In DAMPA, to enhance the premature convergence avoidance ability, the predator crowding degree ranking and comprehensive learning strategies were adopted in the second stage to maintain the population diversity and thereby inhibit premature convergence. Additionally, a stage-independent control of the stepsize-scaling strategy that uses different control parameters in three stages was designed to balance the exploration and exploitation abilities. Two case experiments were conducted to evaluate the proposed algorithm. Compared with the latest algorithm, in the first case, DAMPA reduced the makespan and energy consumption by 21.06% and 23.47% at most, respectively. In the second case, the makespan and energy consumption are reduced by 34.35% and 38.60% on average, respectively. Meanwhile, the algorithm achieved greater throughput in both cases.