In this paper we numerically approximated the field-effect mobility of a-Si:H TFT. Field-effect mobility, based on the charge-trapping model and new effective capacitance model in our study, used Chebyshev approximation was approximated as the function of gate potential(gate-to-channel voltage). Even though various external factors are changed, this formula can be applied by choosing the characteristic coefficients without any change of the approximation formula corresponding to each operation region. Using new approximated field-effect mobility formula, the dependences of field-effect mobility on materials and thickness of gate insulator, thickness of a-Si bulk, and operation temperature in inverted staggered-electrode a-Si:H TFT were estimated. By this was the usefulness of new approximated mobility formula proved.