In this paper the mechanisms of a temporal electrohydrodynamic axisymmetric instability of non-Newtonian dielectric liquid jets moving through a dielectric gas with surface tension gradient have been investigated. The dispersion relation between the nondimensional growth rate and the nondimensional wave number for the eight-constant Oldroyd model is derived using appropriate boundary conditions. The effects of different parameters such as Ohnesorge number, Weber number, elasticity number, deformation retardation to stress relaxation ratio, gas to liquid density ratio, gas to liquid velocity ratio, electric field, and the dielectric constants of the two media on the stability behavior of the system are discussed in detail. Comparisons between the cases of absence or presence of electric field, non-Newtonian fluids, surface tension gradient, and gas to liquid velocity are achieved. The present work is a good foundation for the invistigations of the instability and breakup of non-Newtonian liquid jets with electric field effect and surface tension gradient existence.