Degenerate dense plasmas are of great interest due to their important applications in modern technology and astrophysics. Such plasmas have generated a lot of interest in the last decade owing to their importance in many areas of physics such as semiconductors, metals, microelectronics, carbon nanotubes, quantum dots, and quantum wells. Besides, degenerate plasmas present very interesting features for fusion burning waves’ ignition and propagation. In this paper, we investigated the effects of static magnetic field on energy states and degeneracy of electrons in dense plasma. Using perturbation theory, two cases are considered, strongly and weakly magnetized electrons. Strong magnetic field will not eliminate completely the degeneracy, but it functions to reduce degeneracy. Perturbed energy eigenvalues ΔE are calculated to high accuracy. Besides, regardless of whether the perturbed state is degenerate or not, the energy ΔE is given by considering the average of orbital and spin coupling Ws=ℵrL→·S→ with respect to the eigenfunction Ψn,l,m,ms. Here L→ is the angular momentum vector, S→ is the spin vector of electrons, and ℵr is the energy of spin orbit coupling in plasma, which plays a crucial role in the study of energy states and degeneracy of plasma electrons.