A fastening structure for securing a heatsink module is provided. The structure includes at least a first fastening piece attached to the circuit board and having a first fastening member, a heat spreader having its attached side connected to the heatsink module, hence able to swing vertically, and a pair of first positioning members protrudingly provided on the thermal spread; a second fastening piece having a second fastening member to connect to the first fastening member and a fulcrum to suppress the heat spreader, the second fastening piece having suitable elasticity for the second fastening member to swing vertically and axially around the fulcrum; and a suppressing member having a pair of second positioning members to engage the first positioning members and having a portion press against the top of fulcrum to ensure the state of engagement between the first fastening piece and the second fastening piece.