Dark Matter experiments are recently focusing their detection techniques in low-mass WIMPs, which requires the use of light elements and low energy threshold. In this context, we present the TREX-DM experiment, a low background Micromegas-based TPC for low-mass WIMP detection. Its main goal is the operation of an active detection mass $sim$0.300 kg, with an energy threshold below 0.4 keVee and fully built with previously selected radiopure materials. This article describes the actual setup, the first results of the comissioning in Ar+2%iC$_4$H$_{10}$ at 1.2 bar and the future updates for a possible physics run at the Canfranc Underground Laboratory in 2016. A first background model is also presented, based on Geant4 simulations and a muon/electron discrimination method. In a conservative scenario, TREX-DM could be sensitive to DAMA/LIBRA and other hints of positive WIMPs signals, with some space for improvement with a neutron/electron discrimination method or the use of other light gases.