To understand the effect of given radial electric field on ion-temperature gradient driven mode (ITG) stability in tokamak plasmas, we derive the eigenmode equation for ITG including the poloidal rotation and density modulation associated with radial electric field by using nonlinear gyrokinetic theory. The equation is solved for the eigenfrequency, growth rate and parallel mode structure of ITG both in short- and long-wavelength limit with energetic-particle-induced geodesic acoustic mode (EGAM) as a specific form. The eigenmode equation is not only solved analytically, but also solved numerically to validate the analytic solutions. It is found that, the radial electric field induced poloidal rotation can significantly stabilize ITG, while the density perturbation of the radial electric field may slightly distort the ITG parallel mode structure, but has little effect on ITG stability. The result is consistent with the common picture of turbulence suppression by poloidal shear flow. The general model is also applicable to the investigation of the indirect interaction of ITG and energetic particle driven Alfvén instabilities via zonal structures generation, by introducing poloidal rotation and density modulation associated with zonal structures spontaneously excited by Alfvén instabilities. The indirect channel is supplement to the direct interaction of microturbulences and energetic particle driven Alfvén instabilities.