Context. A new challenging adaptive optics (AO) system, called multi-object adaptive optics (MOAO), has been successfully demonstrated on-sky for the first time at the 4.2 m William Herschel Telescope, Canary Islands, Spain, at the end of September 2010. Aims. This system, called CANARY, is aimed at demonstrating the feasibility of MOAO in preparation of a future multi-object near infra-red (IR) integral field unit spectrograph to equip extremely large telescopes for analysing the morphology and dynamics of high-z galaxies. Methods. CANARY compensates for the atmospheric turbulence with a deformable mirror driven in open-loop and controlled through a tomographic reconstruction by three widely separated off-axis natural guide star (NGS) wavefront sensors, which are in open loop too. We compared the performance of conventional closed-loop AO, MOAO, and ground-layer adaptive optics (GLAO) by analysing both IR images and simultaneous wave-front measurements. Results. In H-band, Strehl ratios of 0.20 are measured with MOAO while achieving 0.25 with closed-loop AO in fairly similar seeing conditions (r0 ≈ 15 cm at 0.5 μm). As expected, MOAO has performed at an intermediate level between GLAO and closed-loop AO.