Abstract. We report the magnetization curve under magnetic fields H up to 30 T at low temperatures in a tetrahedral spin-chain system Cu₃Mo₂O₉ single crystal. This material shows successive phase transitions to an antiferromagnetic phase at T_N = 7.9 K and a weak ferromagnetic (WF) phase at T_c 2.5 K in low magnetic fields. As the magnetic field increases below T_N two rapid increases in magnetization occur at 0 – 0.1 and 19.3 T for H//a and 0.3 – 0.8 and 17.5 T for H//c. However, these increases do not occur for H//b. These facts refute the conventional spin flop transition. The rapid increases disappear above T_N. The magnetic moments are canted toward the ac plane by the Dzyaloshinskii-Moriya interaction in the WF phase. Consequently, these rapid increases in magnetization at high magnetic fields are interpreted by sudden rotations of the WF moments around the b axis.