A prototype of a beam position and phase measurement system is designed for the proton accelerator in the China Accelerator Driven Sub-critical system (ADS). The signals from the Beam Position Monitor (BPM) detector are narrow pulses with a repetition frequency of 162.5 MHz and the input amplitude would vary for more than 40 dB. By applying the high-speed high-resolution analog-to-digital conversion technique, the input radio-frequency (RF) signals are directly under sampled to orthogonal streams by precisely adjusting the sampling clock frequency. Compared with the traditional method to obtain the in-phase and quadrature-phase (IQ) data, it simplifies both the analog and digital processing circuits. All signal processing algorithms are integrated within one field programmable gate array (FPGA) chip for a good system simplicity. Initial testing results indicate that this prototype achieves a phase resolution better than 0.03° and a position resolution better than 5 μm over the input amplitude range from -44 dBm to -4 dBm, well beyond the requirement.