Long-term transmission network expansion planning aims to determine where, when and which types of equipment should be installed over a period of time, in order to meet the electric market needs with certain specifications of quality in services at the lowest possible cost. Until now, several methods have been proposed to solve the Static Transmission Network Expansion Planning (STNEP) problem, considering a multi-voltage approach using the DC load flow, however, these solutions may not be feasible when the AC model is used for the operational problem. In this paper a multi-stage model based on the mathematical formulation of the AC load flow is solved, considering a multi-voltage approach, power losses and reactive power compensation. The AC multi-stage transmission network expansion planing problem with multi-voltage approach (MTNEP-MV) was solved by the hybrid meta-heuristic, Differential Evolution (DE) and Continuous Population-Based Incremental Learning (PBILc) algorithm. To evaluate the proposed mathematical formulation Garver 6-bus system was used. The results show that raising the transmission system voltage and considering the MTNEP-MV problem, less transmission lines are required, and also power losses and reactive power compensation needs, are reduced.