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The widespread popularity of mobile computing devices, such as Laptops, handheld devices and cell phones, as well as recent advances in the wireless communication technologies have motivated researchers to provide novel solutions and applications for the users that were previously not feasible. The users of these mobile computing devices expect the same features and services from these devices as were previously available from conventional desktop computers. However to provide mobility and reduction of size of these mobile devices, the battery life is a major concern; several hardware based techniques have been proposed which results in more energy efficient systems as compared to the earlier systems. Even after these hardware improvement based techniques the problem still persists and it is believed that software based techniques have enough potential to reduce the energy demand to overcome the problems faced due to energy limitation. In this paper, we look into the problem of distributing the computational tasks among different devices in hybrid network environment. By hybrid networks we mean a network containing both wired as well as wireless handheld devices. The reason of selecting hybrid network environment is because most of the applications of mobile devices require accessing resources on the high bandwidth unlimited energy devices connected on wired network to help conserve the energy utilization of the energy limited wireless handheld devices. We have proposed a novel energy-aware scheduling algorithm to solve the problems of resource constrained mobile devices. Our scheduling algorithm schedules a set of computational tasks which may have operational and communication dependencies, into the set of heterogeneous devices so as to minimize both the energy consumption and time taken by the tasks to be completed. Experiments show that significant improvement in the over all performance in terms of energy consumption and execution time of the handheld devices can be achieved by using our algorithm. [ABSTRACT FROM AUTHOR]