In quantum precision measurement applications–where low-amplitude signal fluctuations must be detected with the highest accuracy–precise conversion of low-frequency analog inputs is essential. Nonlinearity and phase noise in voltage-controlled oscillators (VCOs) are known to limit the linearity and accuracy of VCO-based analog-to-digital converters (VCO-ADCs). In this work, we employ an LC-VCO with intrinsically low phase noise in combination with a closed-loop differential pulse-code modulation (DPCM) feedback architecture to mitigate both phase noise and nonlinearity. Specifically, a controlled bias is applied to the VCO input using asynchronous Graycode counting and a digital predictor, enabling compression of the VCO input dynamic range. Combined with first-order noise shaping and a moderate oversampling ratio, this approach achieves a high dynamic range without resorting to higher-order loop designs. The system integrates a differential LC-VCO module, a low-jitter clock source, a precision amplifier, and a high-resolution DAC. Experimental results demonstrate a spurious-free dynamic range (SFDR) of 109 dB and a signal-to-noise-and-distortion ratio (SNDR) of 104 dB, corresponding to a 17-bit effective number of bits (ENOB), over a 100 Hz bandwidth.