The aim of this paper is to calculate the analytical form of the equation of state for dilute relativistic plasma. We obtained the excess free energy and pressure in the form of a convergent series expansion in terms of the thermal parameter μ where μ = mc^2/KT, m is the mass of charge, c is the speed of light, K is the Boltzmann’s constant, and T is the absolute temperature. The results are discussed and compared with previous work of other authors.