A new type of continuous transesterification reactor has been designed, built and tested (numerically and experimentally) with the aim of producing biodiesel from the conversion of rapeseed oil. This reactor is an alternative solution to the batch system. It is based on a three-dimensional S-3D geometry. The flow in this geometry is chaotic, with a laminar regime. This reactor has a very high oil-to-biodiesel conversion efficiency. It is around 94% for almost all operating conditions in terms of reaction temperature and oil flow rate. The physical and chemical properties of biodiesel, such as viscosity, flash point and cetane number, comply with international standards (ASTM D6751 and EN 14214). In addition to its interesting physical and chemical properties, our system continuously produces 13.5 kg/h of biodiesel.