The fine-structure intervals of Na principal series np(n=39) are calculated by the many-body perturbation theory (MBPT) within the framework of relativity. To deal with the problem that a large set of continuum states is required in the MBPT calculation, an exponential potential is employed to generate a discrete, finite and nearly complete set of numerical basis functions. The zeroth-order wavefunctions and eignvalues are obtained by solving the relativistic Hartree-Fock (RHF) equation and the RHF equation with the action of a potential barrier. The basis set used in this work contains intermediate orbitals with the angular momentum l 6 and in an appropriate energy range, and most of them are the so called contracted orbitals. Encouraging results are obtained using this technique to calculate the second-order correlation corrections, combining the Breit effects in a first-order perturbation approach. Compared with other theoretical calculations, the present results are much close to the experimental results.