Most current studies formulate the cloud workflow scheduling as a single-objective or multi-objective optimization problem with at most three objectives, which is unable to fully meet practical scenarios′ needs. To address the limitations above, many-objective cloud workflow scheduling model was established, where many indicators such as time, cost, reliability, resource consumption, load balancing, were taken into account. Then, an improved co-evolutionary algorithm was introduced to address this problem, where dual-stage search strategy and multi-indicator cooperation mechanism were employed to effectively balance the convergence and diversity of solution set, so as to enhance the search capability of algorithm. Experiments on seven types of real life workflow instances reveal that our proposal outperforms the existing peers and can find better scheduling schemes in most cases.