The problem of constructing of the Sobolev orthogonal polynomials s α r,n(x) generated by Charlier polynomials s α n (x) is considered. It is shown that the system of polynomials s α r,n(x) generated by Charlier polynomials is complete in the space Wr lρ , consisted of the discrete functions, given on the grid Ω = {0, 1, . . .}. Wr lρ is a Hilbert space with the inner product hf, gi. An explicit formula in the form of s α r,k+r (x) = P k l=0 b r l x [l+r] , where x [m] = x(x − 1). . .(x − m + 1), is found. The connection between the polynomials s α r,n(x) and the classical Charlier polynomials s α n (x)in the form of s α r,k+r (x) = U r k · s α k+r (x) − rP−1 ν=0 V r k,νx [ν] ¸ , where for the numbers U r k , V r k,ν we found the explicit expressions, is established.