Two compounds (Tb(1-x)Mn(y))MnO(3-δ) (W1, x = 0.089, y = 0.063; W2, x = 0.122, y = 0.102) have been synthesized by solid-state method and characterized using neutron diffraction and magnetic measurements. They crystallize in space group Pnma at room temperature and Pna21 at low temperature. W1 shows a sinusoidal antiferromagnetic order, and W2 shows both sinusoidal and canted commensurate antiferromagnetic orders. The magnetic moments of the commensurate antiferromagnetic order for W2 are antiferromagnetically coupled along the a- and c-axes, and ferromagnetically coupled along the b-axis in the Pna21 setting. Strong ferromagnetic response is induced by doping more Mn into the Tb site of (Tb(1-x)Mn(y))MnO(3-δ).