We report InSb-based high-speed photodetectors grown on GaAs substrate. The p-i-n type photodetectors can operate at room temperature. Room-temperature dark current was 4 mA at 1 V reverse bias, and the differential resistance at zero bias was 65 Omega. At liquid nitrogen temperature, the dark current was 41 muA at 1 V reverse bias and the differential resistance at zero bias was 150 kOmega. Responsivity measurements were performed at 1.55 mum wavelength at room temperature. The responsivity increased with applied bias. At 0.6 V, responsivity was 1.3 A/W, where unity quantum efficiency was observed with internal gain. Time-based high-speed measurements were performed using a pulsed laser operating at 1.55 mum. The detectors showed electrical responses with 40 ps full width at half maximum, corresponding to a 3 dB bandwidth of 7.5 GHz.