Here we report the structural, magnetic, dielectric and transport properties of Ba2FeCrO6 (BFCO) double perovskite oxides synthesized via solid-state reaction method. Rietveld refinements of X-ray powder diffraction data revealed that the BFCO oxides crystallized in hexagonal crystal structure (P6(3)/mmmc). The BFCO powders exhibited a spherical morphology with an average size of 600 nm. Fourier transform infrared spectrum verified both edge-shared (Cr/Fe)O-6 octahedra and corner-shared (FeO4) tetrahedron in the powders. XPS spectra confirmed the oxidation states of various elements in the powders. The saturation magnetization and coercive field of the powders at 5 K were 0.41 emu/g and 665 Oe, respectively. The magnetic T-C and T-N were 330 K and 24 K, respectively. A butterfly-shaped magnetoresistance (MR)- H curve observed in BFCO ceramics at 2 K, was resulted from the intergranular magneto-tunneling effect. The MR (2 K, 7 T) was -3.29%. Temperature dependent resistivity of BFCO ceramics displayed a semiconducting behavior, and the electrical transport properties were well fitted by Mott's variable range hopping model, thermally activated semiconductor conductivity model, and small polaron hopping model, respectively. A strong frequency dispersion dielectric behavior was observed in BFCO ceramics, which had a dielectric constant of similar to 610 at 1 MHz and dielectric loss of 0.84 at room temperature. A dielectric abnomality observed around 378 K at low frequencies was ascribed to the charge carriers trapped by oxygen vacancies, while a broad and diffuse phase transition at high frequencies appeared due to the random positionings of Fe and Cr cations at B-site.