We report on an experimental demonstration of laser wakefield electron acceleration using a sub-TW power laser by tightly focusing 30 fs laser pulses with an 8 mJ pulse energy on a 100 mu m scale gas target. The experiments are carried out at an unprecedented 0.5 kHz repetition rate, allowing 'real-time' optimization of accelerator parameters. Well-collimated and stable electron beams with quasi-monoenergetic peaks in the 100 keV range are measured. Particle-in-cell simulations show excellent agreement with the experimental results and suggest an acceleration mechanism based on electron trapping on the density downramp, due to the time-varying phase velocity of the plasma waves.