One of the most critical issues in overhead cranes is the swing of a suspended load while the crane starts to move and accelerates, changes the movement direction, breaks or stops. This can lead to severe damage, and therefore several methods have been applied to damp the load swings. Most of these methods are based on information about the swing angle of a suspended load. In traditional methods, camera vision, acceleration or inclinometers sensors, simple pendulums and other types of sensors have been used. Generally, a method is desired if it can estimate the swing angle with the least equipment costs, while using an uncomplicated calculation method and the minimum sensitivity to environmental situations and industrial noises. In this paper, a new algorithm is proposed to estimate the swing angle. To do so, the supplied voltage and current of the induction motor which drives the trolley are measured, and then using a new proposed method based on a dynamic analysis of the mathematical dynamic model, the swing angle is estimated and is used in the controller system to damp the swings. The proposed method is verified by means of computer simulations.