High Energy Physics experiments require fast and efficient methods toreconstruct the tracks of charged particles. Commonly used algorithms aresequential and the CPU required increases rapidly with a number of tracks.Neural networks can speed up the process due to their capability to modelcomplex non-linear data dependencies and finding all tracks in parallel.In this paper we describe the application of the Deep Neural Networkto the reconstruction of straight tracks in a toy two-dimensional model. It isplanned to apply this method to the experimental data taken by the MUonEexperiment at CERN.