SW China Normal Univ, Dept Phys, Chongqing 400715, Peoples R China
; Chinese Acad Sci, Inst High Energy Phys, Beijing 100039, Peoples R China
; Chinese Acad Sci, Shanghai Inst Nucl Res, Shanghai 201800, Peoples R China
Debye screening mass st the next-to-leading order is studied by the resummation method based on perturbation theory at finite temperature. We find that the critical temperature for the J/psi dissociation is 0.211 GeV. The contributions from the next-to-leading order are important, and critical temperature and chemical potential are shifted lower values.