To solve a system of linear algebraic equations with a positive definite matrix arising from discretization of elliptic boundary value problems, the author suggests a variant of the multigrid algorithm with coarse spaces constructed by the aggregation of unknowns and smoothing. The performance of the algorithm is further improved by a variant of an overcorrection proposed originally by \textit{R. Blaheta} [J. Comput. Appl. Math. 24, No. 1/2, 227-239 (1988; Zbl 0663.65106)]. The convergence theory for a two-level algorithm is given. Results of numerical experiments indicate that the method presented is efficient.