The SU(N) symmetric antiferromagnetic Heisenberg model with multicolumn representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of a Young diagram with two columns, we confirm that a valence-bond solid (VBS) order appears as soon as the Neel order disappears at N = 10, indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for either the Neel or the VBS ordering for N >= 15. This is actually consistent with the large-N theory, which predicts that the VBS state immediately follows the Neel state, because the expected spontaneous order is too weak to be detected.