Scheduling for directed acyclic graph (DAG) tasks with the objective of minimizing makespan has become an important problem in a variety of applications on heterogeneous computing platforms, which involves making decisions about the execution order of tasks and task-to-processor mapping. Recently, the chemical reaction optimization (CRO) method has proved to be very effective in many fields. In this paper, an improved hybrid version of the CRO method called HCRO (hybrid CRO) is developed for solving the DAG-based task scheduling problem. In HCRO, the CRO method is integrated with the novel heuristic approaches, and a new selection strategy is proposed. More specifically, the following contributions are made in this paper. (1) A Gaussian random walk approach is proposed to search for optimal local candidate solutions. (2) A left or right rotating shift method based on the theory of maximum Hamming distance is used to guarantee that our HCRO algorithm can escape from local optima. (3) A novel selection strategy based on the normal distribution and a pseudo-random shuffle approach are developed to keep the molecular diversity. Moreover, an exclusive-OR (XOR) operator between two strings is introduced to reduce the chance of cloning before new molecules are generated. Both simulation and real-life experiments have been conducted in this paper to verify the effectiveness of HCRO. The results show that the HCRO algorithm schedules the DAG tasks much better than the existing algorithms in terms of makespan and speed of convergence.