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The method for camera motion estimation is proposed for the moving objects. Whereas the estimation of the structure and motion (SaM) of the moving objects usually involves the constraints on the motion of the camera and the object, the moving camera velocities can be estimated in our work using the images of the moving object from the single camera without any constraint on the camera and object motion. To this end, the dynamics of the partially measurable state are arranged in such a way that the recursive least-squares (RLS) algorithm can be employed for stationary objects and then the nonlinear observer based on RISE (robust integral signed error) method for dynamic objects sequentially. The proposed method has advantages in that when the proposed method and the previously developed SaM algorithms are combined together, we can reconstruct the 3-D structure of the moving objects from 2-D images from a single camera. Simulation results under time-varying velocities of both camera and object are presented to verify the proposed method.