The precise simulation of interannual variability of East Asian summer monsoon (EASM) is still a challenge for the state-of-the-art models. In this study, based on the recent proposed potential vorticity circulation (PVC) theory, we find that the second mode of the multivariate empirical orthogonal function (MV-EOF) for the observed East Asian Summer Monsoon (EASM) has a close relationship with the first mode of the cross-equatorial PVC (CEPVC) and the cross-tropopause PVC (CUPVC). Based on observational analysis, we further evaluate the simulation capability of the second mode of the East Asian Summer Monsoon (EASM) in July from the FGOALS-f3-L historical experiment and analyze the potential causes of the bias. Results indicate that the model fails to reproduce the meridional dipole pattern of geopotential height and precipitation of EASM which is closely related to the simulation of the CUPVC bias. Further analysis suggests that the correct simulation of the convergence and divergence of the water vapor flux which related to the changes in CUPVC is the key physical process for the model to accurately simulate the second mode of EASM. The results also indicate the improvement in the simulation of the CUPVC related to the South Asian High (SAH) phenomenon could improve the simulation skill of the interannual variability of EASM.