A connector with a heat sink to prevented a card from being damaged due to friction when the card is inserted or removed includes a frame provided with two guide arms and two elastic members, each guide arm containing two chutes, each chute containing an upper and a lower limit zones; a pressurizing-down mechanism connected to the frame, a leading post received in the chute being disposed on each side arm, and a heat sink being provided on top; card insertion driving the pressurizing-down mechanism to move with its leading post in the chute for the heat sink to contact the card to conduct the heat generated from the card; and the elastic member moving the pressurizing-down mechanism into the upper limit zone to remove the card.