The effects of electric-quadrupole (E2) transitions on ion energy-level populations in plasma are studied by constructing the collisional radiative model of a three-level atomic system in the steady-state approximation. It is found that the influence is non-negligible at the low electron density, and becomes larger when the E2 transition rate grows with atomic number increasing. Furthermore, we investigate the E2-transition effects on the populations of levels in the ground configuration for Fe-like Mo¹⁶⁺ and U⁶⁶⁺ ions in an electron-beam ion-trap plasma. The level populations are obtained by solving the large-scale rate equation numerically. On this basis, we discuss the influence of the E2 transition on the line intensity ratio of the magnetic dipole (M1) lines. In addition, we point out the significance of the E2 transitions on the intensity ratio of the M1 lines that can be used to diagnose the electron density of plasma.