© 2022, Pleiades Publishing, Ltd.Abstract: This article is devoted to the construction of a parallel multigrid algorithm for the numerical solution of (non)linear initial-boundary value problems (implicit schemes) based on a robust multigrid technique (RMT). A distinctive feature of the proposed algorithm is the possibility of the parallel solution of initial-boundary value problems and initial-boundary value problems in a unified manner involving 3m independent computers (threads, if the OpenMP parallelization technology is used), m = 1, 2, 3, …. Coarse grids are built only in space, the number of grid levels depends on the conditionality of the coefficient matrix of the resulting system of linear algebraic equations (SLAEs). The Seidel method with the point ordering of the unknowns is used as a smoothing procedure for solving the initial-boundary value problem for a heat equation with constant coefficients. A description of the algorithm and the results of the computational experiments performed using the OpenMP technology are given.