The special mass shift coefficients and field shift factors for the atomic transitions 3s2S1/2-3s2P1/2 and 3s2S1/2-3s2S3/2 of Mg+ ion are calculated by the relativistic multi-configuration interaction method, and the isotope shifts are also obtained for the Mg+ isotopes with the neutron numbers 8 N 20. Our calculations are carried out by using the GRASP2 K package together with the relativistic isotope shift computation code package RIS3. In our calculations the nuclear charge distribution is described by the two-parameter Fermi model and the field shifts are calculated by the first-order perturbation. In order to generate the active configurations, a restricted double excitation mode is used here, the electron in the 3s shell (3s1) is chosen to be excited, another electron is excited from the 2s or 2p shells (2s22p6), and the two electrons in the inner 1s shell (1s2) are not excited. The active configurations are expanded from the occupied orbitals to some active sets layer by layer, each correlation layer is labeled by the principal quantum number n and contains the corresponding orbitals s, p, detc. The maximum principal quantum number n is 6 and the largest orbital quantum number lmax is g. According to our calculations, the normal mass shift coefficients are -586.99 GHzamu and -588.50 GHzamu, the special mass shift coefficients are -371.90 GHzamu and -371.95 GHzamu, the field shift factors are -117.10 MHzfm-2 and -117.18 MHzfm-2 for the 3s2S1/2-3s2P1/2 and the 3s2S1/2 -3s2S3/2 transitions of Mg+ ions, respectively. Then the isotope shifts for different Mg+ isotopes are obtained using the available data of the nuclear mass and the nuclear charge radii. Our results are coincident with other theoretical calculations and also with experimental results. The relative errors of our calculations are in a range from 0.13% to 0.28% compared with the latest measurements. Our calculations are the most consistent with the experimental measurements for the moment. The results provided here in this paper could be referred to for the experimental and theoretical study of Mg+ isotope shift, and they could be applied to the spectral measurement experiments of the short-lived Mg+ isotopes and also used for the research of the characteristics of exotic nuclei with Mg+ isotopes near the magic neutron numbers N=8 and N=20. The calculation method and the excitation mode used here could also be extended to other multi-electron systems with eleven orbital electrons, and the corresponding theoretical studies of the atomic spectral structures and isotope shifts could then be carried out.