The aim of this work is to introduce new ways to model the I-V characteristic of a PV cell or PV module using straight lines and Bézier curves. This is a complete novel approach, Bézier curves being previously used mainly for computer graphics. The I-V characteristic is divided in three sections, modeled with lines and a quadratic Bézier curve in the first case and with three cubic Bézier curves in the second case. The result proves to be accurate and relies on the fundamental points usually present in the PV cell datasheets: Voc (the open circuit voltage), Isc (the short circuit current), Vmp (the maximum power corresponding voltage) and Imp (the maximum power corresponding current) and the parasitic resistances Rsh0 (shunt resistance at Isc) and Rs0 (series resistance at Voc). The proposed algorithm completely defines all the implied control points and the error is analyzed. The temperature and irradiance influence is also analyzed. The model is also compared using the least squares fitting method. The final validation shows how to use Bézier cubic curves to accurately represent the I-V curves of an extensive range of PV cells and arrays.