A traversable wormhole generally violates the averaged null energy condition, typically requiring exotic matter. Recently, it was discovered that a traversable wormhole can be realized with non-exotic matter in Einstein-Dirac-Maxwell theories in flat space. This study extends the discussion to AdS spacetime and finds traversable wormholes with spherical and planar topologies. Furthermore, based on the AdS/CFT correspondence, we compute the entanglement entropy of strips and disks on the two AdS boundaries of the wormhole. We find that the entanglement entropy undergoes a phase transition as the subsystem size increases.