Terahertz sensing plays an important role in industry, biology and material science. Most existing techniques for terahertz detection either require bulky optics or need cryogenic cooling, and the uncooled thermal detectors usually suffer from long integration times (1-1,000 ms). We propose, and experimentally demonstrate, a novel scheme based on photoacoustic detection of terahertz pulse radiation. The transient and localized heating in a carbon nanotube-polymer composite by the absorption of terahertz pulse energy produces ultrasound, which is subsequently detected by a highly sensitive acoustic sensor. In contrast to conventional thermal detectors utilizing continuous heat integration, this new method of terahertz detection responds to the energy of each individual terahertz pulse by a time-gated scheme, thus rejecting the continuous radiation from the ambient. In addition, this novel detector possesses advantages such as room-temperature operation, a fast response (∼1/40.1 μs) allowing real-time detection, compact size (millimetre scale) and wide spectral response.