Quick tracking in nano-manipulation has been attracting increasing attention among scientific researchers and engineers because it can significantly enhance the effectiveness and efficiency of nano-manipulation. The main reasons that hinder the improvement of accuracy and efficiency of nano-manipulation are the lack of effective real-time tracking and unavoidable perturbations by uncertainties and nonlinearities in the manipulation system. In this paper, we present a new strategy based on compressive sensing to realize quick real-time tracking nano-manipulation trajectory, and build a new kinematic model for objects to be manipulated to overcome the effect of tip positioning and contacting biases on nano-manipulation with AFM. With this approach, the deviation of the object from the predesigned trajectory during the manipulation can be corrected with up to two-thirds of time less than the traditional method, and the object can be smoothly moved to any destination in the nano-space. The approach requires no priori knowledge about the system, environment, and objects being manipulated. It is validated that this strategy works for both hard regular objects and soft irregular samples by experiments.