In this work, we study systematically the mass splittings of the qqQQ (q = u, d, s and Q = c, b) tetraquark states with the color-magnetic interaction by considering color mixing effects and estimate roughly their masses. We find that the color mixing effect is relatively important for the J P = 0 + states and possible stable tetraquarks exist in the nnQQ (n = u, d) and nsQQ systems either with J = 0 or with J = 1. Possible decay patterns of the tetraquarks are briefly discussed.