The energy levels and transition parameters of Li-like quartet states 1s2snl and 1s2pnl′ (l=s, p, d; l′=s, p, d, f; n=2-7) pertaining to 4Po and 4Le (L=S, P, D) Rydberg series in S13+ ion are calculated using a multi-configuration Rayleigh-Ritz variation method. Relativistic effects and mass polarization contributions are taken into account by using the first-order perturbation theory. The quantum electrodynamics (QED) effects and higher-order relativistic corrections are considered to obtain accurate energy levels by the screened hydrogenic formula. The transition oscillator strengths, transition rates, and wavelengths of electric-dipole transitions for 1s2sns4Se-1s2lnl′ 4Po and 1s2snp+1s2pns+1s2pnd4Po-1s2lnl′ 4Le (L=S, P, D) in S13+ ion are systematically calculated and compared with available reference data. Our calculated results will provide valuable data for related experiments in the future.