In this paper, a compact direction-finding system based on a deep neural network (DNN) with a single-patch multi-beam antenna is proposed. To achieve multiple beams, the patch is divided into four sectors by metal vias, and the pattern is tilted in the theta direction due to the coupled mode of the divided patch structure. This design allows a single-patch multi-beam antenna to generate eight beams using a combination of four excitation ports assigned to the four-divided sectors. This approach increases the amount of training data required for DNN-based direction finding without requiring multiple antennas, thus improving the accuracy of estimation probability. Furthermore, compared to our previous work, the parasitic elements are applied to improve the estimation probability by reducing the beamwidth of the antenna. The size of the antenna for the proposed direction-finding system is 0.44λ × 0.44λ × 0.008λ with a 97.7% estimation probability. The direction-finding performance has been validated and compared through the experiment to show higher accuracy with compactness than previously studied works.