Today, many high performance computing plat-forms use hybrid architectures combining multi-core processors and hardware accelerators like GPUs (Graphic Processing Units). This paper presents a new method for scheduling tasks for biological sequence comparison applications with CPUs and GPUs. This strategy is called SWDUAL and is based on a dual approximation scheme for determining which tasks are most suitable to be executed on the GPUs. The objective is to obtain fast execution time and minimize the idle time on each PE (Processing Element). It is implemented using a master-slave model. Results obtained when sequences were compared to five public genomic databases show that this method allows to reduce the execution time on hybrid platforms when compared to other public available implementations.