High quality electron beams have been produced in a laser-plasma accelerator driven by femtosecond laser pulses with a peak power of 26 TW. Electrons are produced with an energy up to 150 MeV from the 2 mm gas jet accelerator and the measured rms relative energy spread is less than 1%. Shot-to-shot stability in the central energy is 3%. Pepper-pot measurements have shown that the normalized transverse emittance is ~1π mm mrad while the beam charge is in the range 2–10 pC. The generation of high quality electron beams is understood from simulations accounting for beam loading of the wakefield accelerating structure. Experiments and self-consistent simulations indicate that the beam peak current is several kiloamperes. Efficient transportation of the beam through an undulator is simulated and progress is being made towards the realization of a compact, high peak brilliance free-electron laser operating in the vacuum ultraviolet and soft x-ray wavelength ranges.