Implantable wireless neural recording microsystems have demonstrated their efficacies in neuroscience studies in the past decades. However, with the advances of neurobiology, higher sensitivity and higher precision neural recording microsystems are becoming the critical need. A biopotential amplifier is the first stage of a neural recording microsystem, the performance of which decides the signal-to-noise ratio and the power dissipation of each recording-channel. In this paper, we present a low-noise biopotential amplifier with a noise efficiency factor (NEF) optimized closer to the theoretical limit of a folded cascode structure. A high transconductance input nMOSFET pair is designed to guarantee a low input-referred noise. A self-biased scheme comprising a weak positive feedback and a strong negative feedback is employed to further enhance the transconductance. By optimizing the noise performance while maintaining the NEF value close to the theoretical limit, a very low input-referred noise and a higher power-noise efficiency are achieved in our design. Using a standard 0.13-μm CMOS process, the proposed amplifier achieves an input-referred noise of 1.98 μVrms at the expense of 7.5 μW power, corresponding to a NEF of 2.31. The gain of the proposed amplifier is 40.84 dB at a -3 dB bandwidth from 6.65 Hz to 9.38 kHz.