Zeeman spectra of the strongly perturbed lines between the B (1)PI and c (3)SIGMA+ states of Nak were measured by the Doppler-free laser polarization spectroscopy. Magnetic field dependence of the Zeeman pattern was studied and the line shapes were found to change remarkably because of the mixing of the B (1)PI and c (3)SIGMA+ states. The patterns of Zeeman splitting were found to be different depending on whether the level was located on the high energy side or the low energy side of the interacting level. The observed Zeeman spectra were studied by taking account of the spin-orbit, hyperfine, and Zeeman interactions. The Zeeman spectroscopy is shown to be useful to analyze the perturbation between the excited states.