The electronic, magnetic and optical properties of double perovskites Pb₂XOsO6 (X=Co, Ni) have been studied by using density functional theory within generalized gradient approximation. By replacing Co from Pb₂CoOsO₆ (PCOO), Pb₂NiOsO₆ (PNOO) is formed. With electron doping, we observed electronic and magnetic phase transition as PCOO and PNOO are found to be A-type anti-ferromagnetic and ferrimagnetic materials having metallic and half metallic features respectively. We noticed significant changed in band structure and density of state as we apply coulomb correlation (U) as well as spin orbit coupling. We calculated the real and imaginary part of dielectric function, optical conductivity and loss function and finally analyzed inter-band transition to the optical properties with band structure.