The ground-state properties of the recent reported proton emitter ¹Tm have been studied within the axially or triaxially deformed relativistic mean field (RMF) approaches, in which the pairing correlation is taken into account by the BCS-method with a constant pairing gap. It is found that triaxiality and pairing correlations play important roles in reproducing the experimental one proton separation energy. The single-particle level, the proton emission orbit, the deformation parameters =0.22 and =28.98 deg. and the corresponding spectroscopic factor for ¹Tm in the triaxial RMF calculation are given as well.