A fast start-up low-voltage bandgap reference voltage generator uses two current generators to provide a first current having a positive temperature coefficient and a second current having a negative temperature coefficient, respectively, and a resistor to generate a temperature independent output voltage according to the sum of the first and second currents. The current generator for providing the first current has a self-bias circuit which uses a single MOSFET to establish the first current, and thereby avoids error caused by mismatched MOSFETs.