For crane loads swing problems, mainly discussed the effect of vertical movement of the load on shimmy, established the mathamatical model of crane load sway under permitted supposed conditions.,through coordinate transformation, transformd differential equation into the standard form of Hill equation, and with research on Hill equation we can get the condition about damped oscillation. Finally, with the introduction of the parameter plane, the stable map of Hill equation can be drawed, i.e. the map of crane load damped oscillation.The results show that, if control of the pendulum length is used to realize the anti-sway of crane，three parametrics including initial pendulum length、amplitude of variation and periodic variation of pendulum length should be considered comprehensively, a coordinate point can be calculated by these three parametrics in the parametric plane，if this point is in the area of damped oscillation in the parameter plane, the anti-sway of crane can be realized.