With the development of cloud computing, the coexistence of multiple cloud service providers appears in the current cloud market. Due to heterogeneous instance types, different bandwidths and various price models among multiple clouds, it is a challenging issue to schedule a deadline-constrained scientific workflow across multiple clouds. Existing research for workflow scheduling are mostly in the traditional distributed computing environment (such as grid), and only a few primal contributions are made in the cloud environment. This paper proposes a scheduling strategy for a deadline-constrained scientific workflow across multiple clouds. In order to minimize the execution cost of the workflow while meeting its deadline, our strategy utilizes the discrete particle swarm optimization technique, and adopts randomly two-point crossover operator and randomly single point mutation operator of the genetic algorithm. Besides, the strategy optimizes the performance for both computation cost and data transfer cost across multiple clouds. Our strategy is evaluated through well-known workflows, and experimental results show that it performs better than other state-of-the-art strategies.