We have investigated the magnetic and dielectric properties of BaCo2Si2O7 single crystal with a quasi-one-dimensional structure to explore novel magnetoelectric functionality. The Weiss temperatures estimated in paramagnetic region are -20K (H∥c) and -74K (H⊥c), indicating the large magnetic anisotropy due to the highly anisotropic structure. The weak ferromagnetic magnetization rises up at 21K, where the dielectric constant perpendicular to the c-axis decreases concomitantly. In addition, we have observed the magnetocapacitance effect below 21K. Δε(H)/ε(0) reaches 0.2% at 5.5K. These results suggest that there exists a substantial coupling between magnetism and dielectricity.