In this paper, the effect of density gradient on the Weibel instability growth rate is investigated. The density perturbations in the near corona fuel, where temperature anisotropy, g, is larger than the critical temperature anisotropy, gc, (g > gc), enhances the growth rate of Weibel instability due to the sidebands coupled with the electron oscillatory velocity. But for g < gc, the thermal spread of the energetic electrons reduces the growth rate. Also, the growth rate can be reduced if the relativistic parameter (Lorentz factor) is sufficiently large, c > 2. The analysis shows that relativistic effects and density gradient tend to stabilize the Weibel instability. The growth rate can be reduced by 88% by reducing g by a factor of 100 and increasing relativistic parameter by a factor of 3
