Evidence demonstrates a link exists between the East Asian winter monsoon (EAWM) and the following East Asian summer monsoon (EASM). Previous studies have found that the EAWM and the following EASM are only closely linked in ENSO years. However, all these studies are based on the hypothesis that the atmosphere's response to ENSO is symmetric. In fact, we demonstrate ENSO plays an asymmetric role in the EAWM-EASM link. This study divides the variability of the EAWM into an ENSO-related part (EAWM_EN) and ENSO-unrelated part (EAWM_RES). The results demonstrate that during strong EAWM_EN conditions (i.e., La Niña events), an anomalous cyclone persists from winter to summer over the western North Pacific (WNP), which can cause a weak EASM in the following summer. In contrast, during weak EAWM_EN conditions (i.e., El Niño events), an anomalous anticyclone persisting from winter to summer is observed over the WNP. However, the anomalous anticyclone's intensity is much stronger than the counterpart and is located more southward. As a result, the intensity of EASM anomalies is stronger during weak EAWM_EN years. This asymmetry may be attributed to the different evolutions of the SST anomalies over the tropical Pacific Ocean and the North Indian Ocean. During strong EAWM_EN conditions, the SST anomalies in the tropical central-eastern Pacific decay slowly and thus significant signals still persist in the following summer, which contribute to the persistence of the WNP anomalous cyclone in the following summer. However, during weak EAWM_EN conditions, the SST anomalies decay quickly in the tropical Pacific, while the Indian Ocean warms significantly in the following summer. Thus the anomalous anticyclone in the WNP results from the significantly warmed Indian Ocean through the "capacitor mechanism".