This article presents a new asynchronous least-significant-bit (LSB) averaging technique to improve the signal-to-noise ratio (SNR) of high-precision successive-approximation-register (SAR) analog-to-digital converters (ADCs) with high power efficiency. After normal conversion, a linear searching is performed to coarsely reduce the conversion error asynchronously. Subsequently, the comparator performs a complementary number of comparisons with unchanged residue voltages to further reduce the error. Compared to traditional statistical noise reduction methods, the proposed method is insensitive to process, voltage, and temperature (PVT) variations since it does not require knowledge of the noise distribution. Additionally, it only slightly reduces the signal bandwidth as only 10 extra cycles are required. Therefore, the proposed method is suitable for low-noise, high-resolution SAR ADCs with MS/s speed. The proposed technique is implemented on a 16-bit SAR ADC in a 180-nm CMOS process. Running at 1 MS/s with the proposed technique, the measured signal-to-noise-and-distortion ratio (SNDR) is improved from 91.8 dBFS to 95.1 dBFS, and the dynamic range (DR) is improved from 93.8 dB to 98.1 dB. With power increased by 6.2% and period increased by 11%, this technique leads to a 2.59 dB Schreier figure-of-merit (FoM(SNDR)) and a 3.59 dB FoM(DR) improvement. The ADC consumes 7.1 mW and achieves a 173.6-dB FoM(SNDR) and a 176.6-dB FoM(DR), respectively.