Development of transistors for advanced low noise amplifiers requires better understanding of mechanisms governing the charge carrier transport in correlation with the noise performance. In this paper, we report on study of the carrier velocity in InGaAs/InP high-electron-mobility transistors (HEMTs) found via geometrical magnetoresistance in the wide range of the drain fields, up to 2 kV/cm, at cryogenic temperature of 2 K. We observed, for the first time experimentally, the velocity peaks with peak velocity and corresponding field decreasing significantly with the transverse field. The low-field mobility and peak velocity are found to be up to 65000 cm2/Vs and 1.2x106 cm/s, respectively. Extrapolations to the lower transverse fields show that the peak velocity can be as high as 2.7x107 cm/s. The corresponding intrinsic transit frequency can be up to 172 GHz at the gate length of 250 nm. We demonstrated, for the first time, that the low-field mobility and peak velocity reveal opposite dependencies on the transverse field, indicating the difference in carrier transport mechanisms dominating at low- and high-fields. Therefore, the peak velocity is an appropriate parameter for characterization and development of the low noise HEMTs, complementary to the low-field mobility. The results of the research clarify the ways of the further development of the HEMTs for advanced applications.