A switchable bidirectional core-actuated valve is provided with a chamber, and a first shaft hole, a second shaft hole and an output hole communicating with the chamber. The chamber is received therein with a non-return valve able to move in the chamber. Thus, water cooling liquid can make use of water pressure to have the non-return valve moving to a first position or a second position. When the non-return valve is at the first position, the first shaft hole will communicate with the output hole, when at the second position, the second shaft hole will communicate with the output hole. Thus, water cooling liquid can get into the chamber through the first shaft hole or the second shaft hole and then flow out of the output hole.