The effects of different spin-orbit interaction on entanglement of a two-qutrit Heisenberg XX system with inhomogeneous magnetic fields were investigated by means of negativity. It is found that with increasing of the Dzialoshinskii-Moriya (DM) interaction, entanglement increases at high temperature, while it fluctuates at low temperature. In general case, the entanglement of x component Dzialoshinskii-Moriya (DM) interaction is higher than that of z component and it is on the contrary under certain conditions. So, entanglement can be controlled by varying the directions of DM interaction. Also quantum logic gate can be realized by using the symmetry and transition of entanglement.