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At present, with the enormous development of cloud-based applications, the demand of related enterprises for computing and a large number of storage resources is increasing day by day. Due to the characteristics of ultra-large scale and low cost, cloud computing has been gradually applied to complex workflow scheduling problems in various fields. The traditional scheduling algorithms have lot of limitations such as inefficient task management and unreasonable resource allocation. The workflow scheduling problem in the cloud computing environment has been proved to be an NP-complete problem. To solve these problems, this paper proposes an improved ant colony optimization workflow scheduling for workflow execution of tasks within a user-specified deadline. On this basis, a hybrid cloud deadline-constrained cost workflows scheduling algorithm under the hybrid cloud is proposed, which will prioritize scheduling execution in the private cloud, and use the public cloud to schedule part of the workflow when the task execution time exceeds the task deadline constraint. The simulation results show that the proposed workflow scheduling algorithm reduces the cost and attain faster execution time.