Compact, table-top sized accelerators are key to improving access to high-quality beams for use in industry, medicine and academic research. Among laser-based accelerating schemes, the inverse free-electron laser (IFEL) enjoys unique advantages. By using an undulator magnetic field in combination with a laser, GeV m À 1 gradients may be sustained over metre-scale distances using laser intensities several orders of magnitude less than those used in laser wake-field accelerators. Here we show for the first time the capture and high-gradient acceleration of monoenergetic electron beams from a helical IFEL. Using a modest intensity (B10 13 Wcm À 2 ) laser pulse and strongly tapered 0.5 m long undulator, we demonstrate 4100 MV m À 1 accelerating gradient, 450 MeV energy gain and excellent output beam quality. Our results pave the way towards compact, tunable GeV IFEL accelerators for applications such as driving soft X-ray free-electron lasers and producing g-rays by inverse Compton scattering.