In this paper we consider the system of polynomials (l_r,n)^a (r — natural number, n = 0,1,...), orthonormal with respect to the Sobolev inner product (Sobolev orthonormal polynomials) of the following type<f, g> = (sum _(v=0))^(r−1) f^(ν)(0)g ^(ν)(0) + (f _0)^∞ f^(r) (x)g^(r)(x)ρ^(x)dx and generated by the classical orthonormal Laguerre polynomials.Recurrence relations are obtained for the system of Sobolev orthonormal polynomials, which can be used for studying various properties of these polynomials and calculate their values for any x and n.