This paper uses the hybrid cloud architecture, including the local cloud and the remote public cloud, to execute the mobile tasks with the objective of optimizing the resource allocation, while meeting the service‐level agreement requirement. Hybrid cloud is a cloud computing environment that uses a mix of on‐premises http://searchcloudcomputing.techtarget.com/definition/private-cloud and third‐party http://searchcloudcomputing.techtarget.com/definition/public-cloud services with orchestration between the 2 platforms. The mobile application could run in private cloud, but use http://searchcloudcomputing.techtarget.com/definition/cloud-bursting to access additional computing resources from a public cloud when computing demands spike. The proposed Quality of Service–based resource allocation optimization scheme across local and public cloud for resource‐constrained mobile device is formulated into a constrained optimization problem and further divided into 2 subproblems, ie, one for resource allocation for the local cloud and one for the remote public cloud, using the Lagrange method. The proposed Quality of Service–based resource allocation optimization algorithm across local and public cloud is proposed. Through the experiments, the performance of proposed algorithm is evaluated with other baseline algorithms. The results of the experiments show a performance improvement when compared to the approaches from the literature.