This study reveals a pronounced out-of-phase relationship between surface air temperature (SAT) anomalies over northeast Eurasia in boreal winter and following summer during 1980-2017. A colder (warmer) winter over northeast Eurasia tends to be followed by a warmer (cooler) summer of next year. The processes for the out-of-phase relation of winter and summer SAT involve the Arctic Oscillation (AO), the air-sea interaction in the North Atlantic Ocean, and a Eurasian anomalous atmospheric circulation pattern induced by the North Atlantic sea surface temperature (SST) anomalies. Winter negative Arctic Oscillation (AO)/North Atlantic Oscillation (NAO)-like atmospheric circulation anomalies lead to continental cooling over Eurasia via anomalous advection and a tripolar SST anomaly pattern in the North Atlantic. The North Atlantic SST anomaly pattern switches to a dipolar pattern in the following summer via air-sea interaction processes and associated surface heat flux changes. The summer North Atlantic dipolar SST anomaly pattern induces a downstream atmospheric wave train, including large-scale positive geopotential height anomalies over northeast Eurasia, which contributes to positive SAT anomalies there via enhancement of downward surface shortwave radiation and anomalous advection. Barotropic model experiments verify the role of the summer North Atlantic SST anomalies in triggering the atmospheric wave train over Eurasia. Through the above processes, a colder winter is followed by a warmer summer over northeast Eurasia. The above processes apply to the years when warmer winters are followed by cooler summers except for opposite signs of SAT, atmospheric circulation, and SST anomalies.