Particle accelerators are used in a wide variety of fields, ranging from medicine and biology to high-energy physics. The accelerating fields in conventional accelerators are limited to a few tens of MeV m(-1), owing to material breakdown at the walls of the structure. Thus, the production of energetic particle beams currently requires large-scale accelerators and expensive infrastructures. Laser-plasma accelerators have been proposed as a next generation of compact accelerators because of the huge electric fields they can sustain (>100 GeV m(-1)). However, it has been difficult to use them efficiently for applications because they have produced poor-quality particle beams with large energy spreads, owing to a randomization of electrons in phase space. Here we demonstrate that this randomization can be suppressed and that the quality of the electron beams can be dramatically enhanced. Within a length of 3 mm, the laser drives a plasma bubble that traps and accelerates plasma electrons. The resulting electron beam is extremely collimated and quasi-monoenergetic, with a high charge of 0.5 nC at 170 MeV.