In this paper, an analytical expression of nonlinear power amplifier characteristic based on orthogonal polynomials method for filter bank multicarrier modulation (FBMC) systems is proposed. FBMC has been widely deployed for broadband wireless communications. Nevertheless, one of the drawbacks of the FBMC systems is a large peak-to-average power ratio (PAPR) in its time domain signal. This leads to a nonlinear distortion when the signal is passed through a high power amplifier (HPA) of a transmitter. In this paper, an analytical computation of the HPA characteristic based on the orthogonal polynomial method for baseband uniform, exponential, and Rayleigh input distribution with odd and even polynomial coefficient order is proposed. The HPA modelling error comparison between the proposed orthogonal method and the conventional polynomial method is investigated at a different IBO. Simulation results show that the proposed orthogonal polynomial method is superior to the conventional polynomial method. Moreover, the HPA modelling error of the proposed orthogonal polynomial method for uniform input distribution yield better result compared with the exponential and the Rayleigh input distribution case.