Abstract: An Impedance converter is an important part of the design of broadband power amplifiers in modern wireless communication systems. A design method of Legendre impedance transformer based on transmission matrix is proposed. This method combined with the normalized transfer matrix theory completes the formula derivation and design steps of the Legendre impedance transformer. Combined with MATLAB, ADS (Advanced Design System) jointly designed a three-order Legendre impedance transformer with an impedance ratio of 4 and a relative bandwidth of 66.7%. The third-order Legendre impedance converter has an in-band attenuation L of less than 0.013 dB and an actual bandwidth of 2 GHz.