In electron-positron plasmas some of the plasma modes are decoupled due to the equal charge to mass ratio of both species. The dispersion properties of the propagation of linear waves in degenerate electron–positron magnetoplasma are investigated. By using the quantum hydrodynamic equations with magnetic fields of the Wigner–Maxwell system, we have obtained a set of new dispersion relations in which ions’ motions are not considered. The general dielectric tensor is derived using the electron and positron densities and its momentum response to the quantum effects due to Bohm potential and the statistical effect of Femi temperature. It has been demonstrated the importance of magnetic field and its role with the quantum effects in these plasmas which support the propagation of electromagnetic linear waves. Besides, the dispersion relations in case of parallel and perpendicular modes are investigated for different positron-electron density ratios.