We developed a cross-shaped structure with a multilayer film for the 3D atom trap. The spatial profile of near-field light produced in the center gap was obtained from the finite difference time domain simulations, and the trap potential for a single Rb atom was also calculated. Based on the results, we determined the angle of slope, the radius of curvature of edges in the center, the thickness of each layer, and the size of the trap space. In keeping with the design, the cross-shaped structure with the trap space of 400 nm x 140 nm was fabricated through dry-etching process including focused-ion-beam milling and gold sputtering. The depth of the trap potential was estimated to exceed 10 uK in terms of temperature, which is easily obtained by using the standard laser-cooling techniques, from the approximate calculations with the WKB method. In addition, we evaluated the trapping time of the cold Rb atom to be over 20 seconds from numerical estimations of trap loss processes involving tunneling of the thin potential barrier and collision with background gaseous atoms. Nanophotonics has a potential to lead to tremendous breakthrough in nano-scale science.