A method for winding a synthetic yarn coming from an extruder including the steps of connecting at least one yarn exiting from an extruder with at least one corresponding bobbin rotatable around a longitudinal axis thereof, on which the yarn is wound; rotating the bobbin by imparting a specific speed and/or torque to the bobbin; measuring a value of the tension acting on the yarn upstream of the bobbin; adjusting the speed and/or the torque to maintain the measured tension value substantially equal to a constant reference value of the tension.