Today, research on mobile robot control and navigation is focused on plenty of analytical approaches through control loop integration of various controllers, path planning algorithms, and ending with machine learning approaches, genetic and optimization algorithms, and finally on artificial neural network applications. In the paper, there is a concept and design process of a neural network that can guide a differential-drive robot towards a virtual target that moves along different path shapes without the use of any other traditional control loop or algorithms. The dataset to train the neural network is collected by running a series of numerical simulations based on an artificial potential field approach as reference control and applying a number of various path scenarios and the tracked target’s speed. As a result, a guidance artificial neural network (GNN) with a specified number of neurons in the hidden layer and a type of activation function was found. GNN can guide a robot in any case of path shape and speed, even if it was not considered in the training process. The ability of GNN to drive robot tracking of a virtual target is proven by a series of numerical simulations. The results achieved of the proposed control approach, where the GNN is the only controller applied to the robot's guidance, can be utilized to design more complex neural network struc-tures. In such structures, outputs of another higher neural network can be used as a source of input data for the GNN, giving, i.e., the coordinates of the tracked point. This approach enables the possibility of the creation of a hierarchical bio-inspired control structure, allowing for the introduction of a term of AI-driven robot guidance, which will be the subject of future work.