Scheduling of scientific workflows on hybrid cloud architecture, which contains private and public clouds, is a challenging task because schedulers should be aware of task inter-dependencies, underlying heterogeneity, cost diversity, and virtual machine (VM) variable configurations during the scheduling process. On the one side, reaching a minimum total execution time or makespan is a favorable issue for users whereas the cost of utilizing quicker VMs may lead to conflict with their budget on the other side. Existing works in the literature scarcely consider VM’s monetary cost in the scheduling process but mainly focus on makespan. Therefore, in this paper, the problem of scientific workflow scheduling running on hybrid cloud architecture is formulated to a bi-objective optimization problem with makespan and monetary cost minimization viewpoint. To address this combinatorial discrete problem, this paper presents a hybrid bi-objective optimization based on simulated annealing and task duplication algorithms (BOSA-TDA) that exploits two important heuristics heterogeneous earliest finish time (HEFT) and duplication techniques to improve canonical SA. The extensive simulation results reported of running different well-known scientific workflows such as LIGO, SIPHT, Cybershake, Montage, and Epigenomics demonstrate that proposed BOSA-TDA has the amount of 12.5%, 14.5%, 17%, 13.5%, and 18.5% average improvement against other existing approaches in terms of makespan, monetary cost, speed up, SLR, and efficiency metrics, respectively.