The unparalleled catalytic activity of carbonic anhydrases (CAs) towards CO2 hydrolysis can potentially contribute to carbon capture, utilization, and storage technology aimed at global decarbonization; however, the high cost and low stability of CAs significantly limit their practical applications. Recently, the development of robust and effective nanozymes with CA-mimicking activity has been proposed as a promising solution to this challenge. Herein, a novel zinc-based organophyllosilicate (ZnAC) nanozyme with CA-like catalytic activity was synthesized by a facile one-pot sol–gel method for the first time, leading to a Zn-O coordination structure that mimicked the catalytic center fragments of natural CAs, with surface amino groups acting as the affinity sites and proton shuttles. The synergistic effect of the two components on the open surface of the layered structure resulted in excellent CA-like activity with a Michaelis–Menten constant (Km) of 4.071 mM, maximum velocity (Vmax) of 0.220 mM/s, and turnover number (kcat) of 11.213 /s at 25 °C and pH=7.5, which were superior to those of most previously reported CA-like nanozymes. The catalytic performance of ZnAC significantly improved with increasing pH and temperature; furthermore, ZnAC exhibited excellent stability, maintaining high catalytic activity after the exposure to extreme temperatures or pH values, eight reaction cycles, and 30 d of storage. Additionally, ZnAC significantly increased the rate of CO2 hydration and the extent of CO2 mineralization and precipitation. This work proposes a new strategy for designing and constructing efficient CA-like nanozymes, providing valuable insights into the structure–activity relationship and new perspectives for the implementation of CO2 fixation.