Triple-GEM detectors are a well known technology in high energy physics. In order to have a complete understanding of their behavior, in parallel with on-beam testing, a Monte Carlo code has to be developed to simulate their response to the passage of particles. The software must take into account all the physical processes involved from the primary ionization up to the signal formation, e.g. the avalanche multiplication and the effect of the diffusion on the electrons. In the case of gas detectors, existing software such as GARFIELD already perform a very detailed simulation but are CPU time consuming. A description of a reliable but faster simulation is presented here: it uses a parametric description of the variables of interest obtained by suitable preliminary GARFIELD simulations and tuned to the test beam data. It can reproduce the real values of the charge measured by the strip, needed to reconstruct the position with the Charge Centroid method. In addition, particular attention was put to the simulation of the timing information, which permits to apply also the micro-Time Projection Chamber position reconstruction, for the first time on a triple-GEM. A comparison between simulation and experimental values of some sentinel variables in different conditions of magnetic field, high voltage settings and incident angle will be shown.