One-dimensional laser range profiles (LRPs) contain abundant information regarding the shape, size, and attitude of detected objects. For a dynamic conical target, the variation of its size and attitude could have a significant effect on the projections of LRP peaks. Ground coordinates, target coordinates, and incident field coordinates are established to compute the LRP of dynamic cones. In order to inverse the size, a genetic algorithm is adopted. The cone heights and half-cone angles of three different cones are inversed. Moreover, the results are used to inverse the attitude angles at any sampling time in order to verify accuracy of the theory. The inversion mentioned in this paper can be applied in any targets of arbitrary material, shape, and attitude with great efficiency.