This paper presents a new efficient and robust method for the automatic design of Metasurface (MS) by using a Deep Neural Network (DNN), which has less complexity and design time compared to conventional MS design methods. The main contribution of the present method is its ability the design reflective/transmissive MS for wave manipulation in a wide range of frequencies (12 GHz - 18 GHz). To this end, several multi-bit encoded MSs are provided that are of potential interest in single/multi-beam, Orbital Angular Momentum (OAM), and Phase Gradient Metasurface (PGM) antenna applications. In each case, the proposed DNN provides the required unit cell in two transmission and reflection modes from 12 GHz to 18 GHz for different targets. In order to demonstrate the performance of the proposed DNN method, the following steps are implemented: (i) first, the architecture of the DNN method and the creation of pixelated unit cells by DNN are discussed. This step presents 3-bit coded unit cells to design Intelligent Reflective Surfaces (IRS) in wireless communication systems. (ii) several single/multibeam reflective OAM and transmissive PGM high gain antenna structures are presented. (iii) In order to validate the proposed design concept, a Transmissive PGM lens antenna prototype with 22.6 dBi gain and Aperture Efficiency (AE) of 40% is experimentally tested at 14 GHz. Simulation and measurement results are in good agreement, which confirms the accuracy of the proposed method. The proposed DNN method can be considered a new reliable approach for designing reflective/transmissive MSs in applications of antenna and microwave with their highly demanding market.