Void fraction is one of the dominant parameters of gas-water two-phase flow. Its accurate measurement plays an important role in achieving parameter control and reliable operation in industrial processes. This article proposes a more practical method for the measurement of void fraction in gas-water bubbly flow using a derived multi-eigenvalue sequence from normalized EIT impedance matrix. The relations between eigenvalues and void fraction, bubble radius, number of bubbles are investigated by numerical simulations, which illustrates the superiority of using multi-eigenvalue rather than the largest eigenvalue for void fraction prediction. The nonlinear mapping between the multi-eigenvalue sequence and void fraction is established by applying the XGBoost model with a sliding window of time series. This proposed method is verified by static and dynamic experiments using a self-developed setup in our laboratory, generating stable gas-water bubbly flow with void fraction less than 0.12. It is shown that the proposed method can predict void fraction with a relative deviation of 10%. Compared with the conventional method based on largest eigenvalue, the proposed method efficiently improves the measurement accuracy of void fraction in gas-water bubbly flow and applicability in actual measurement of two-phase flow, which can be further extended to other flow regimes.