An edge-based smoothed finite element method (ES-FEM) is proposed to solve 3D acoustic problems in the mid-frequency range, using the simplest linear tetrahedron meshes that can be generated automatically for complicated geometry. In present ES-FEM, the gradient smoothing operation is performed with respect to each edge-based smoothing domain, which is also serving as building blocks in the assembly of the stiffness matrix. It turns out the ES-FEM provides an ideal amount of softening effect, and significantly reduces the numerical dispersion error in low- to mid-frequency range. Several numerical examples demonstrate the superiority of the ES-FEM for 3D acoustic analysis, especially at mid-frequency.