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We present a new measurement of the Newtonian gravitational constant G based on cold-atom interferometry. Freely falling samples of laser-cooled rubidium atoms are used in a gravity gradiometer to probe the field generated by nearby source masses. In addition to its potential sensitivity, this method is intriguing as gravity is explored by a quantum system. We report a value of G= 6.667× 10− 11 m 3 kg− 1 s− 2, estimating a statistical uncertainty of±0.011× 10− 11 m 3 kg− 1 s− 2 and a systematic uncertainty of±0.003× 10− 11 m 3 kg− 1 s− 2. The long-term stability of the instrument and the signal-to-noise ratio demonstrated here open interesting perspectives for pushing the measurement accuracy below the 100 ppm level.