The time dependant density functional theory(TDDFT) and local density approximation (LDA) are used to calculate the transition spectra of sodium atom. Several excited energy levels of valence-electron and the corresponding electronic wave function distribution are calculated in detail. The characteristic transition Rydberg series spectra of sodium are given. The calculated results agree with the experiment data very well, which is a good evidence for the applicability of TDDFT to the description of the excited system.