We report a novel phenomenon of a surface-induced phase transition in salt-free solutions of charged colloids. We develop a theory of this effect and confirm it by Molecular Dynamics simulations. To describe the colloidal solution we apply a primitive model of electrolyte with a strong asymmetry of charge and size of the constituent particles - macroions and counterions. To quantify interactions of the colloidal particles with the neutral substrate we use a short-range potential which models dispersion van der Waals forces. These forces cause the attraction of colloids to the surface. We show that for high temperatures and weak attraction, only gradual increase of the macroion concentration in the near-surface layer is observed with increase of interaction strength. If however temperature drops below some threshold value, a new dense (liquid) phase is formed in the near-surface layer. It can be interpreted as a surface-induced first-order phase transition with a critical point. Using an appropriately adopted Maxwell construction, we find the binodal. Interestingly, the observed near-surface phase transition can occur at the absence of the bulk phase transition and may be seemingly classified as prewetting transition. The reported effect could be important for various technological applications where formation of colloidal particle layers with the desired properties is needed.