We introduce a system of stacked two-dimensional electron and hole gas layers with Rashba spin orbit interaction and show that the tunnel coupling between the layers induces a strong three- dimensional (3D) topological insulator phase. At each of the two-dimensional bulk boundaries we find the spectrum consisting of a single anistropic Dirac cone, which we show by analytical and numerical calculations. Our setup has a unit-cell consisting of four tunnel coupled Rashba layers and presents a synthetic strong 3D topological insulator and is distinguished by its rather high experimental feasibility.