Recently, theoretical studies have indicated that BaFe2Se3 may host a ferrielectric polarization and an uncompensated ferroelectricity driven by the exchange striction in its magnetic block order. Here, structural, magnetic, electrical transport, dielectric, and magneto-dielectric properties in the BaFe2Se3 single crystals were systematically investigated. Below 320 K, BaFe2Se3 is a semiconductor, and the thermal activated transport processes with different activation energies were used to describe the conductivities in high and low temperature ranges. Magnetization measurements show a crossover from a short-range antiferromagnetic correlation to a long-range antiferromagnetic order at around 230 K and another antiferromagnetic transition at 150 K. The dielectric constant can be changed by about 6% in a magnetic field of 8 T. However, the ferrielectric characteristics of BaFe2Se3 are difficult to be fully verified by electric polarization and dielectric measurements, which may be related to the quite narrow energy gap and low resistivity.