The 3D ES-FEM using tetrahedral mesh proposed recently has showed many great features in mechanics, and mid-frequency acoustics analysis, such as kh≈1. When it comes to higher frequencies, the 3D ES-FEM also encounters the dispersion error, which is related to “slightly overly-soft stiffness” induced by the excessive edge-based smoothing operations compared to the continua system. In this paper, an improved 3D edge-based smoothed finite element method (IES-FEM) is proposed by introducing a parameter controlling the ratio of “slightly over-softness” of the ES-FEM and “over-stiffness” of the FEM, and the balance of the discretized system can then be tuned to reduce the dispersion error in higher frequency range, i.e. 1≤kh≤2. Numerical results demonstrate the advantages of IES-FEM for acoustic problems, in comparison with the ES-FEM using the same mesh.