We present efficient high-order harmonic generation (HHG) based on a high-repetition rate, few-cycle, near infrared (NIR), carrier-envelope phase stable, optical parametric chirped pulse amplifier (OPCPA), emitting 6 fs pulses with 9 μJ pulse energy. In krypton, we reach conversion efficiencies from the NIR to the extreme ultraviolet (XUV) radiation pulse energy on the order of ∼10-6 with less than 3 μJ driving pulse energy. This is achieved by optimizing the OPCPA for a spatially and temporally clean pulse and by a specially designed high-pressure gas target. In the future, the high efficiency of the HHG source will be beneficial for high-repetition rate two-colour (NIR-XUV) pump-probe experiments, where the available pulse energy from the laser has to be distributed economically between pump and probe pulses. © 2017 IOP Publishing Ltd.