Based on a sticky-electrolyte model, the Ornstein-Zernike integral equation is solved for nonsymmetric electrolytes with stickiness between ions at various distances equal to or less than the collision diameter. The hypernetted chain or Percus-Yevick approximation is used for the closure inside the hard core, while the mean-spherical approximation for electrostatic interactions is used for the closure outside the hard core. Expressions for correlation functions and thermodynamic properties in term of the sticky parameters are derived. Numerical results are presented for various cases.