In this paper, we focus on energy efficiency (EE) maximization for simultaneous wireless information and power transfer (SWIPT) based energy-constrained and amplify-and-forward (AF) relay networks. We adopt low-complexity time-switching (TS) protocol to realize SWIPT at the energy-constrained relay node, and formulate an EE maximization problem in which TS factor and transmit power control are needed to be jointly optimized. Since the formulated problem is non-convex and difficult to solve, we propose an algorithm combining fractional programming and alternating convex optimization to optimize TS factor and transmit power iteratively with low complexity. Simulation results are provided to demonstrate the convergence of the proposed algorithm, as well as the performance gains in terms of EE compared with other existing schemes.