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We have investigated the magnetotransport properties of the transition metal trichalcogenide TaSe₃, which is a Dirac semimetal candidate. While the electrical resistivity exhibits metallic behavior at zero field, a magnetic field (H)-induced upturn is observed at low temperatures for H > 4 T, applied perpendicular to the current direction. The extremely large, non-saturating transverse magnetoresistance (MR) reaches ~ 7000 % for H = 14 T at 1.9 K. For H > 6 T, Shubnikov-de Haas (SdH) oscillations are observed with frequencies F_α ≈ 98 T and F_β ≈ 186 T. By constructing the Landau fan diagram for each oscillation, we calculated the Berry phase to be 1.1 π and 0.2 π for F_α and F_β , respectively . The underlying physics will be discussed.