In this paper, the synthesis procedufe of impedance matching network is presented for broad-band microwave amplifier design, whereby amplifier operating in the octave bandwidth is designed and fabricated in detail. The transfer function of the matching netowrks is synthesized by chebyshev approximation and element values for the networks of specified topology are calculatd for various MILs and ripples. After the transistor is modeled by negative-image device model, the synthesis procedure for matching networks is applied to broad-band amplifier design which has electrical performance of about 12dB gain in 4 to 8GHz range. Experimental results obtained from the fabricated amplifier are shown to approach the electrical performance designed in the given frequency range. Construction of the impedance matching networks by transfer function synthesis is very useful method for the design of broad-band microwave amplifiers.