A scheduling algorithm of scientific workflow in commercial clouds is proposed. To solve the problem of the existing scheduling algorithms and the slack time allocation strategies that do not consider the OR control structure, the critical activity priority (CAP) is defined. Also the service benefit ratio (SBR) and slack time allocation strategy of activity are presented. Then, from the two levels of definition time and running time, the deadline distribution algorithm of activity is proposed. The results of this study provide a more suitable solution for solving the time-cost optimization problem in the scientific workflow scheduling.