Cloud workflow is one of the most significant patterns, widely applied in tackling with the large-scale complicated computing tasks. In recent years, with the ever-growing scale and complexity of computing tasks, the demand for computing resources has getting higher in a corresponding explosive ascending trend. Cloud computing converges massive computing resources, providing users with on-demand computing services in the form of virtual machines. It undoubtedly serves as a potential ideal runtime environment for workflows. Moreover, Cloud workflow scheduling is devoted to allocating reasonable resources for different workflow tasks to meet the expected scheduling effects and targets. In general, the cloud workflow scheduling objectives involve time, cost, reliability, resource utilization, load balancing and other aspects. However, the current mainstream optimizations, up to now, typically attempt to formulate the cloud workflow scheduling problem as a single objective or multi-objective optimization problem at most three objectives. Whereas, these strategies might be less feasible to address many-objective cloud workflow scheduling problem with more than four objectives. Thus, we directly model cloud workflow scheduling into a many-objective problem, and then introduce a Dual-Stage Improved Co-Evolutionary Algorithm which aims to effectively balance the convergence and diversity, using a dual-stage strategy and various indicator characteristics to provide more affluent decision information for workflow scheduling. Experiments reveal that the proposed algorithm apparently outperforms the existing algorithms, which can find a better scheduling solution in most cases.