The anti-swing problem of the bridge cranes is discussed. The position and anti-swing control strategy based on BVP arithmetic is presented. The position and anti-swing control programming of bridge cranes can be transformed into the two-point boundary value problem (BVP) of nonlinear systems. According to the boundary conditions, the tractive force function of Fourier series form with free parameters is constructed. The BVP is solved with the bvp4c function in Matlab toolbox, and the tractive force sequence is obtained. The presented position and anti-swing control strategy for bridge cranes belongs to open-loop feedforward control essentially. The simulation of anti-swing and position control process illustrates the effectivity of the control strategy.