We report on the first use of undoped bulk-grown p-type GaSb as a low-temperature detector in composite bolometers for the detection of non-equilibrium phonons. In the ohmic regime, the detector's low-temperature resistivity measurements are consistent with the Mott variable-range hopping conduction characterized by ln R(T)∝exp (T₀/T)^1/4 with a temperature coefficient of (-0.42-3.46ln T)^-1 K^-1 in the temperature range 1.4 K≤T≤4.2 K. The detector showed a fast response time of approximately 1 µs and excellent reproducibility. In our opinion, the most promising areas of applications are in nuclear spectroscopy (low-energy x-ray and beta-particle detection) for which small-volume detectors can be used and the study of phonon dynamics in 2DEG structures.