This paper describes the development of a 3-stage cryogenic low noise InP HEMT amplifier for ALMA Band 3 receivers. A detailed design is given using Hughes 0.1 μm low noise InP HEMTs for producing a low power dissipation amplifier, < 9 mW. The amplifier design uses a hybrid circuit in order to provide the flexibility for optimizing the active devices and passive components. The optimal impedance matching for low noise and low input return loss were obtained by computer aided simulation to achieve 5 K noise temperature, 36 dB gain, flatness ±1 dB and -10 dB input return loss at 12 degrees Kelvin in the 4-9 GHz band. The amplifier will be used as a cold IF preamplifier with a SIS mixer in the Band 3 receivers now being constructed for the Atacama Large Millimetre Array (ALMA).