The Fermi surface of InBi was investigated using ultrasonic and differential-susceptibility techniques. Quantum oscillations of the de Haas-van Alphen type were observed in both types of measurements and their frequencies were measured in the (001), (010), and $(1\overline{1}0)$ planes. Several frequencies which were not observed by previous workers have been discovered. These correspond to new portions of the Fermi surface. In addition, more extensive data on frequencies which had been observed earlier were obtained. The largest portion of the Fermi surface which was observed is approximately a prolate ellipsoid of revolution containing 1.9\ifmmode\times\else\texttimes\fi{}${10}^{20}$ carriers/${\mathrm{cm}}^{3}$. It was found that, in many cases, the ultrasonic and differential-susceptibility techniques are sensitive to different electron orbits on the Fermi surface and that therefore these two techniques of studying the Fermi surface complement each other.