We present the tunable resonance behavior of laminated metal mesh metamaterial embedded by barium strontium titanate (BST) thin film. The electromagnetic frequency response shows a redshift when the dielectric constant of BST thin film increases, and the tunability is about 22.6%. For the tunable metamaterial proposed in this paper, the structural unit of metal graphics is used as electrodes to apply the electric potential, which simplifies the preparation and application of tunable THz metamaterials greatly. It has potential application in the THz media modulators.