Mobile computation offloading is emerging as a promising technology to enhance the computation power of mobile devices by borrowing processing resources from the cloud. However, using cloud resource is a double-edged sword because of the potentially enormous network energy consumption of mobile devices. In this paper, we study the mobile device resource management problem for application throughput fairness and energy efficiency in computation offloading environment. Our problem seeks to optimize task arrival rates, scheduling for local processing and offloading, CPU clock speed, and network interface selection, so as to maximize the energy-utility efficiency defined as achievable utility per unit energy consumption. The efficiency metric has a fractional form which is hard to deal with in general. To address this difficulty, we modify general Lyapunov optimization technique and derive a series of shortterm problems, which change over time with respect to an unknown objective parameter. Then we derive an offloading algorithm and prove that the algorithm maximizes the longterm energy-utility efficiency. Trace-driven simulations demonstrate that our algorithm achieves high energy efficiency while maintaining throughput fairness among applications running on a mobile device.