Hydrogen crossover rate has emerged as a key indicator for characterizing the aging process of proton exchange membrane fuel cell. Electrochemical techniques are the most common for quantifying hydrogen crossover. However, for the present, most existing methods are only applicable to the scenario of single fuel cell. There is still a lack of efficient methods for the quantification of hydrogen crossover in stack configuration. In this paper, we establish a galvanostatic charging method with high accuracy and strong operability to measure hydrogen crossover in fuel cell stack for the first time. The fundamentals of this presented method are expounded through comprehensively analyzing the electrochemical processes occurring on fuel cell electrode under galvanostatic conditions. The effectiveness of the galvanostatic charging method is fully validated on a single cell and a multi-cell stack. Furthermore, necessary details for practical implementation of our method are discussed, and a data processing procedure allowing automatic and quick data extraction is correspondingly developed. This new characterization methodology for stack-level fuel cells offers significant advantages of being accurate, high-efficiency and non-invasive, and it will provide a powerful tool for lifespan evaluation, inconsistency analysis and failure diagnosis of fuel cell stacks.