A piecewise curvature-corrected bandgap reference (BGR) with negative feedback is proposed. It features employing a temperature-dependent resistor ratio technique to get a piecewise corrected current, which corrects the nonlinear temperature dependence of the first-order BGR. The piecewise corrected current generator also forms negative feedback to improve the line regulation and power supply rejection (PSR). Measurement results show the proposed BGR achieves a maximum temperature coefficient (TC) of 21.2ppm/℃ without trimming in the temperature range of - 50-125℃ and a PSR of - 60dB at 2.6V supply voltage. The line regulation is 0.8mV/V in the supply range of 2.6-5.6V. It is successfully implemented in an SMIC 0.35μm 5V n-well digital CMOS process with the effective chip area of 0.04mm^2 and power con- sumption of 0.18mW. The reference is applied in a 3,5V optical receiver trans-impedance amplifier.