The conditions for the onset of natural convection (convective instability) in the electrochemical system consisting of two plane horizontal electrodes and solution containing three types of ions between them were analyzed theoretically. The equations of flow of incompressible viscous liquid to the Boussinesq approximation and the equations of material balance with the electroneutrality condition were used as the mathematical model. The set of equations for amplitudes of perturbations was solved using the Galerkin method. The dependences of critical Rayleigh number on the system parameters are obtained for monotonic and oscillatory instabilities in the case that the electrochemical reaction proceeds under the conditions of limiting current. The examples of instability diagrams are presented. In contrast to the binary electrolyte, for a solution containing three types of ions, the critical Rayleigh number depends on the charges of ions and the ratio between the diffusion coefficients of ions in the solution.