High-resolution spectra of the B-1 Pi-->X(1) Sigma(+) transition of (NaRb)-Na-23-Rb-85 molecule are measured by the technique of the Doppler-free optical-optical double resonance polarization spectroscopy (OODRPS). The molecular constants of the X(1) Sigma(+)(v''=5-30) levels are determined, and the potential energy curve is constructed up to v''=30 by the RKR method. The time-resolved fluorescence intensity following the excitation to the B-1 Pi(v'=5,J'=around 20) level is measured, and the lifetime of the B-1 Pi(v'=5) level in collisionless limit is determined to be 17.8 ns. The absolute value of the electric dipole moment of the B-1 Pi-X(1) Sigma(+) transition is determined to be 7.0 D in the region of 3.73 Angstrom<R<4.98 Angstrom. Transition lines to the (1)(3) Sigma(+) state from the B-1 Pi(v'=8,J'=15) level, which is perturbed by the (1)3 Pi(1)(v(0),N=J=15) level, are measured by the Doppler-free OODRPS. The energy spacing between the F-1 and F-3 components of the (1)(3) Sigma(+)(v=4,N=15) level is observed to be smaller than 0.001 cm(-1). The hyperfine splittings, which are described by Hund's case (b(beta s)), are observed, and the hyperfine constants A(Na) and A(Rb) of the (1)(3) Sigma(+)(v=4) level are determined to be 0.0293 and 0.0336 cm(-1), respectively. The hyperfine splittings are identified as originating from the Fermi contact interaction. From the analysis, it is concluded that the electron spins in the (1)(3) Sigma(+) state are almost equally populated to the 5s(Rb) and 3s(Na) orbitals. (C) 1996 American Institute of Physics.