Gravitational waves in the 10–100-mHz band are inaccessible to Earth-based detectors because of seismic noise. Hitherto, the most sensitive detectors in this frequency band have been the Doppler tracking of interplanetary spacecraft1 and excitations of seismic motions in the Earth's surface2,3. Here we propose a new and more sensitive type of Earth-orbiting gravitational-wave detector, called a ‘skyhook’, which would operate in the 10–100 mHz band. The skyhook would consist of two masses, one on each end of a long thin cable with a spring at its centre. As it orbits the Earth, the cable would be stretched radially by the Earth's tidal gravitational field. Gravitational waves would pull the masses apart and push them together in an oscillatory fashion; their motion would be transmitted to the spring by the cable; and a sensor would monitor the spring's resulting motion. (An analogous skyhook, for non-gravitational-wave purposes, was proposed by Colombo4 et al. 10 years ago and is planned for flight on the space shuttle5.