Full-dimensional massive multiple-input multiple-output (MIMO) systems boost sum spectral efficiency by offering orders of magnitude increase in multiplexing gains. In time division duplexing systems, however, the reuse of the uplink training pilots among cells results in channel estimation errors, which lead to downlink inter-cell interference, especially for cell-edge users, even with large numbers of antennas. Handling this interference with conventional network MIMO techniques is challenging due to the high channel dimensionality. Further, large antenna precoding and combining implementation is associated with high hardware complexity. In this paper, we propose multi-layer precoding to enable efficient and low complexity full-dimensional MIMO operation. Multi-layer precoding (i) leverages the directional characteristics of large-scale MIMO channels to manage inter-cell interference with low channel requirements, and (ii) allows for an efficient implementation using low-complexity hybrid analog/digital architectures. We present and evaluate a specific multi-layer precoding design for full-dimensional MIMO systems. Simulation results show the potential gains of multi-layer precoding compared with traditional pilot-contaminated massive MIMO setups despite the low channel knowledge requirements and the low-complexity implementation.