The invention discloses a method for installing a stiffening beam of a suspension bridge over a navigable river and a swing shift system used in the method. The suspension bridge is an earth-anchored suspension bridge of a two-tower three-span structure and comprises a main tower A, a main tower B, a side span part A, a side span part B and a middle span part, and a beam storage yard is arranged at the position, on one side of the main tower A, of a shore base. The installation method includes the following steps that a plurality of winches are arranged at the top of the main tower A and the top of the main tower B respectively, an approach bridge is erected between the beam storage yard and the main tower A, a work platform communicated with the approach bridge is erected on the surface, back on to the approach bridge, of the main tower A, and a transport ship is prepared on the river; the middle span part, the side span part B and the side span part A are installed in sequence, wherein the middle span part is installed in the sequence of approach bridge transport, swing shift lowering, ship transport and lifting connection, the side span part B is installed in the sequence of approach bridge transport, swing shift lowering, ship transport, lifting swing shift and combination connection, and the side span part A is installed in the sequence of approach bridge transport, swing shift positioning and combination connection.