The floating zone technique is a well-established single crystal growth method in materials research, which is able to produce volumetrically large specimens with extremely high purities. However, traditional furnace designs have relied on heating from high-powered bulb sources in combination with parabolic mirrors and hence are constrained to transparent growth chambers with large solid angles of optical access. This results in a stark limitation on achievable processing gas pressures and in turn renders a range of compounds unsuitable for crystal growth by the floating zone technique, either due to excessive volatility or due to metastability. Here, we demonstrate a novel high-pressure laser-based floating zone system (HP-LFZ). The use of lasers for heating allows implementation of a high-strength metal growth chamber, permitting greatly enhanced processing pressures over conventional mirror-based designs, with the current design allowing for pressures up to 1000 bar. We demonstrate a series of example single crystal growths using this design in pressures up to 675 bar, a significant increase over processing pressures attainable in commercially available floating zone systems. The general utility of the HP-LFZ is also illustrated via growths of a range of complex oxides.