The applications, where continuum robots are very useful, such as the inspection of hard to reach tight spaces, jet-engines inspections or applications in medicine, require precise control. This paper focuses on a supervised learning-based positional controller for cable-driven continuum robots. The proposed controller is based on training a feed-forward neural network using positional data. The positional data are gathered from a single kinematic structure by applying 30 000 combinations of cable shortenings and measuring the achieved tip positions of every single one of them. The proposed controller was tested on experimental test bench, using three different kinematic structures. The results show that one of the structures achieved better result, however it was also used for data gathering. The difference in results come from different mechanical and material properties of these structures, even though at some points the measured trajectory was quite close to the targeted one. By evaluating these results, our future work will be focusing on characterising common features and introducing them to the learning process, so that more generalized models can be achieved.