We report the properties of a hydrogen (H2) gas sensor based on platinum (Pt)-coated carbon nanotubes (CNTs) in this paper. To fabricate the Pt–CNT composite sensor, a highly aligned CNT sheet was prepared on a glass substrate from a spin-capable CNT forest, followed by electrobeam (e-beam) deposition of Pt layers onto the CNT sheet. To investigate the effect of Pt on the response of the sensor, Pt layers of different thicknesses were deposited on the CNT sheets. A Pt thickness of 6 nm yielded the highest response for H2 detection, whereas Pt layers thinner or thicker than 6 nm led to a reduction of the surface area for gas adsorption and, consequently, decreased response. The Pt–CNT composite sensor detects H2 concentrations of 3–33% at room temperature and shows reproducible behavior with fast response and recovery times.