We investigate current-induced skyrmion dynamics in the presence of Dzyaloshinskii-Moriya interaction and spin-orbit spin-transfer torque corresponding to various types of spin-orbit coupling. We determine the symmetries of Dzyaloshinskii-Moriya interaction and spin-orbit spin-transfer torque based on linear spin-orbit coupling model. We find that like interfacial Dzyaloshinskii-Moriya interaction (Rashba spin-orbit coupling) and bulk Dzyaloshinskii-Moriya interaction (Weyl spin-orbit coupling), Dresselhaus spin-orbit coupling also has a possibility for stabilizing skyrmion and current-induced skyrmion dynamics. (C) 2017 Elsevier B.V. All rights reserved.