The hybrid cloud extends the private cloud model by using both local and remote resources. The private cloud will rely on the resources leased from public cloud providers for the execution of private cloud applications. The paper presents optimal scheduling across public and private clouds in complex hybrid cloud environment. The contributions of this paper have three aspects. 1) The proposed hybrid cloud scheduling policy considers the benefits of private cloud applications and public cloud provider, it can adapt to the changes in the system to find the scheduling optimization. The scheduling optimization is decomposed and conducted across the private cloud and public cloud. 2) Secondly, The paper describes negotiations in hybrid cloud marketplace and gives an example to explain how these rules are resolved by the cloud marketplace. 3) Thirdly, the paper proposes an optimal scheduling algorithm across public and private clouds. The paper also describes negotiations in hybrid cloud marketplace and gives an example to explain how these rules are resolved by the cloud marketplace. In the simulations, the profit of public cloud provider and resource utilization of the proposed algorithm are better than other related works.