The predictions of the response of the vibro-acoustic problems in mid-frequency regime is one of hotspots and difficulties in academy and engineering. However, there is a broad series of mid-frequency vibro-acoustic problems that are not suited to either deterministic methods or statistic methods, due to the complexity of mixed behaviors in this frequency range. An edge-based smoothing technique is applied in the acoustic FEM model to soften the stiffness of whole system. This edge-based smooth finite element method (ES-FEM) is then embedded to achieve a similar hybrid ES-FE-SEA framework. The higher accuracy of proposed ES-FE-SEA comparing with FE-SEA is verified by various numerical examples.