Abstract: The dispersion relation of transverse oscillation in the unmagnetized, collisionless, isotropic and relativistic electronpositron plasma is discussed in the context of q distribution. The dispersion equations in connection with q parameter are derived and then the analytical dispersion laws for ultrarelativistic electronpositron plasma are obtained under the longwavelength approximation and the shortwavelength condition. The dispersion equations are numerically simulated with the purpose of getting the full dispersion curve, and the numerical solutions are coincident with the analytical results in the cases of longwavelength and shortwavelength for ultrarelativistic electronpositron plasma. It is shown that the dispersion relation in the context of q distribution is related to q parameter and temperature, and in the limiting case (q1), the classical dispersion relation based on the Maxwellian distribution is recovered.