Micro-electro-mechanical system (MEMS) pressure sensors play a significant role in pulse wave acquisition. However, existing MEMS pulse pressure sensors bound with a flexible substrate by gold wire are vulnerable to crush fractures, leading to sensor failure. Additionally, establishing an effective mapping between the array sensor signal and pulse width remains a challenge. To solve the above problems, we propose a 24-channel pulse signal acquisition system based on a novel MEMS pressure sensor with a through-silicon-via (TSV) structure, which connects directly to a flexible substrate without gold wire bonding. Firstly, based on the MEMS sensor, we designed a 24-channel pressure sensor flexible array to collect the pulse waves and static pressure. Secondly, we developed a customized pulse preprocessing chip to process the signals. Finally, we built an algorithm to reconstruct the three-dimensional pulse wave from the array signal and calculate the pulse width. The experiments verify the high sensitivity and effectiveness of the sensor array. In particular, the measurement results of pulse width are highly positively correlated with those obtained via infrared images. The small-size sensor and custom-designed acquisition chip meet the needs of wearability and portability, meaning that it has significant research value and commercial prospects.