This paper describes cryogenic 36–45 GHz InP low-noise amplifier monolithic microwave integrated circuits (MMIC's) with an improved noise temperature by eliminating parasitic parallel-plate resonance modes. These MMIC's are used for a Radio Astronomical receiver, which needs the ultimate super low-noise and wide-band frequency characteristics, such as those in ALMA Band 1. The MMIC chips were designed in the coplanar waveguide (CPW), and mounted to the AlN substrate with a flip-chip assembly, which was promising compared to wire bonding. The flip-chip assemblies, however, are prone to cause the parasitic parallel plate resonance mode (PPM). The relationship between the $S$-parameters and the PPM was investigated by using a 3D-electromagnetic simulation of the simple transmission-line test-chip with the same chip size as that of the actual MMIC. In order to eliminate the PPM, additional bumps were mounted on the simple transmission-line test-chip, and the effect of these bumps was confirmed by the simulation. These results obtained from the simple transmission-line test-chip were applied to an actual MMIC chip assembly. The MMIC assembled with the additional bumps had no abnormality in the measured $S$-parameters, and the PPM had been eliminated up to 65 GHz. Moreover, the stability factor, $K$, became more than 2.4 over 36–45 GHz. This InP low-noise amplifier MMIC exhibited a gain of 15 dB and a noise temperature of 180–240 K at room temperature in the frequency range of 36–45 GHz. When cooled to 28 K, a gain of 17 dB and a noise temperature of 22–35 K were obtained at a power consumption of 4.7 mW over 36–45 GHz. A high-gain amplifier module consisting of two cascaded chips, exhibited a gain of 27–30 dB and a noise temperature of 25–30 K at the ambient temperature of 22 K in the frequency range of 41–45 GHz.