By allowing a mobile device to offload computation-intensive tasks to a base station, mobile edge computing (MEC) is a promising solution for saving the mobile device's energy. In real applications, the offloading may span multiple fading blocks. In this paper, we investigate energy-efficient offloading over multiple fading blocks with random channel gains. An optimization problem is formulated, which optimizes the amount of data for offloading to minimize the total expected energy consumption of the mobile device. Although the formulated optimization problem is non-convex, we prove that the objective function of the problem is piecewise convex, and accordingly develop an optimal solution for the problem. Numerical results verify the correctness of our findings and the effectiveness of our proposed method.