A Neural Network (NN) methodology is presented for the Direction of Arrival (DoA) estimation of the desired mobile user, namely the Signal of Interest (SoI), in the asynchronous Direct Sequence Code Division Multiple Access (DS-CDMA) scheme. In DS-CDMA the SoI DoA should be estimated in the presence of a group of interfering users that constitute the Multiple Access Interference (MAI). In this paper a NN algorithm follows the MAI suppression done by the code-matched filters, to achieve the DoA finding goal for a Switched-Beam System (SBS). The proposed method is developed, while DoA estimation simulation tests show accurate results for a varying number of mobile users.