AFM based nanomanipulations have been successfully applied in various areas such as physics, biology and so forth in nano scale. Traditional nanomanipulations always have to approach the problems such as hysteresis, nonlinearity and thermal drift of the scanner, and the noise brought by the position sensor. In this research, a compressive feedbacks based non-vector space control approach is proposed for improving the accuracy of AFM based nanomanipulations. Instead of sensors, the local image was used as the feedback to a non-vector space controller to generate a closed-loop control for manipulation. In this paper, there are four research topics: First, local scan strategy was used to get a local image. Second, since the feedback is an image, a non-vector space controller was designed to deal with the difficulty in vector space such as calibration and coordinate transformation. Third, in order to further decrease the time spent on local scan, compressive sensing was introduced to this system. Finally, to overcome the disadvantage that compressive sensing costs time on reconstructing the original signal, we directly use the compressive data as the feedback. Both theoretical analysis and experimental results have shown that the system has a good performance on AFM tip motion control. Therefore, the non-vector space control method can make visual servoing easier, and the compressive feedback could make a high speed real-time control of nanomanipulation possible. In addition, this new method can be applied to nano-assembly, nano-imaging and nanomanipulation.