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This paper describes the experimental identification of the parameters of the Twin Rotor MIMO System (TRMS) non-linear model using data collected from the real lab set-up. From this non-linear model, a quasi-linear parameter varying (quasi-LPV) model has also been derived using a state transformation. This quasi-LPV model is approximated with a polytopic model using the bounding box approach. Such a model can later be used for control design. The model parameters have been calibrated by means of non-linear least-squares identification approach. Once the calibrated non-linear model has been obtained, a simulator has been built and validated against real data showing satisfactory results when compared to real data.