The upsilon=0-57 levels of the 3p + 3p doubly excited 1 3 Sigma(g)(-) State of Na-2 have been observed by pulsed perturbation facilitated optical-optical double resonance (PFOODR) fluorescence excitation spectroscopy. The T-upsilon=57=39943.5 cm(-1) of the 1(3) Sigma(g)(-), state is 385 cm(-1) above the X(2) Sigma(g)(+) upsilon(+)=0, J(+)=0 ionization threshold and 9 cm(-1) below the Na (3p,P-2(3/2))+Na(3p,P-2(1/2)) dissociation limit. No significant line broadening was observed above the X(2) Sigma(g)(+)upsilon(+)=0,J(+)=0 ionization threshold with our resolution. Molecular constants and the Rydberg-Klein-Rees (RKR) potential curve have been obtained from the observed data. The major constants are T-e=36519.13(17) cm(-1) omega(e)=93.635(41) cm(-1), and B-e=0.11895(90) cm(-1). We have carried out an all-electron ab initio calculation for the 1(3) Sigma(g)(-), State and transition dipole moment for the 1(3) Sigma(g)(-)<->b(3)II(u) system of Na-2. Molecular constants calculated from our ab initio potential curve have reasonable agreement with the experimental constants.