This paper proposes a novel power-efficient light-emitting diode (LED) placement algorithm for indoor visible light communication (VLC). In the considered model, the LEDs can be designedly placed for high power efficiency while satisfying the indoor communication and illumination requirements. This design problem is formulated as a power minimization problem under both communication and illumination level constraints. Due to the interactions among LEDs and the illumination uniformity constraint, the formulated problem is complex and non-convex. To solve the problem, we first transform the complex uniformity constraint into a series of linear constraints. Then an iterative algorithm is proposed to decouple the interactions among LEDs and transforms the original problem into a series of convex sub-problems. Then, we use Lagrange dual method to solve the sub-problem and obtain a convergent solution of the original problem. Simulation results show that the proposed LED placement algorithm can harvest 22.86% power consumption gain when compared with the baseline scheme with centrally placed LEDs.