Ne and Mg isotope chains are investigated based on constrained calculations in the framework of a deformed relativistic mean-field (RMF) model with the NL075 parameter set. The calculated quadrupole deformation and binding energy are compared with other theoretical results as well as the available experimental data. It shows that the calculated deformations of Ne and Mg with the NL075 are more accurate than those obtained with the NL-SH. It is predicted that 19,29,32Ne and 20,31 Mg maybe have a triaxial deformation and 25-28Ne and 27-30Mg exhibit a shape coexistence probably. The closure effect of neutron number N=8 for 20Mg is predicted to be very weak.