We construct the stably stratified magnetized stars within the framework of general relativity. The effects of magnetic fields on the structure of the star and spacetime are treated as perturbations of nonmagnetized stars. By assuming ideal magnetohydrodynamics and employing one-parameter equations of state, we derive basic equations for describing stationary and axisymmetric stably stratified stars containing magnetic fields whose toroidal components are much larger than the poloidal ones. A number of the polytropic models are numerically calculated to investigate basic properties of the effects of magnetic fields on the stellar structure. According to the stability result obtained by Braithwaite, which remains a matter of conjecture for general magnetized stars, certain of the magnetized stars constructed in this study are possibly stable.