There is a scientific debate on the relationship between ancient winter and summer monsoons in East Asia. Some scholars think that East Asian winter and summer monsoons are anti-correlated, and others think not. For this reason, this study is motivated to assess their linkage from the paleoclimate simulation perspective, through analyzing the Last Glacial Maximum (LGM) and mid-Holocene (MH) climate simulated by CCSM3 model. Compared to the present climate, the Aleutian low is found to be deepened and the East Asian winter monsoon (EAWM) is stronger during the LGM winter. The Pacific high in summer is noticed to be weakened and the East Asian summer monsoon (EASM) is weaker at the LGM. During the MH, the Aleutian low and the Asian high in winter are intensified, and the Asian low and the Pacific high in summer are enhanced, indicating that the EAWM and EASM are both stronger than today. Therefore, the EAWM is not always negatively correlated to the EASM. Their relationship may be different at different geological stages. It can be obtained at least from the numerical simulation results that the EAWM and the EASM is negatively correlated during the cooling period, while positively correlated during the warming period.