Burnup calculation plays an essential role in the design of nuclear reactors. It not only allows accurate assessment of fuel depletion to ensure safe and efficient reactor operation but also optimizes fuel utilization to reduce economic costs and minimize environmental impact. Here, we propose a novel physics-constrained dynamic mode decomposition (Pc-DMD)–based neutronics-depletion coupling method to significantly improve the efficiency of burnup calculations. The new method integrates physical constraints into a data-driven dynamic mode decomposition (DMD) model that includes both high-fidelity calculation and Pc-DMD prediction modes. These two modes are iteratively processed through the adaptive coupling of physical constraint terms until the burnup process is completed. In the high-fidelity calculation mode, the physical constraint equations are constructed from the nuclide number density (NND) matrix to quantify the linearity of the depletion system and determine the number of high-fidelity calculation steps. The prediction mode builds a DMD model to predict the NNDs using the NNDs and microscopic reaction rate data provided by the previous high-fidelity calculation mode. Significantly, this eliminates the need for multiple transport calculations. Meanwhile, after selecting the important nuclides by analyzing the contribution of the reaction rates, the number of prediction steps is determined by constructing physical constraints based on the residuals of the NNDs of these nuclides. By calculating the different fuel types and the number of depletion regions, the new method can effectively reduce the number of transport calculations by more than 60% and save 50% to 80% of the total calculation time compared with the traditional burnup calculations while maintaining good calculation accuracy. The method provides a promising solution for high-fidelity burnup calculations in nuclear engineering.