Summary: G. Pfister and J. H. M. Steenbrink [J. Pure Appl. Algebra 77, No. 1, 103–116 (1992; Zbl 0752.14007)] studied the structure of punctual Hilbert schemes of certain degree for irreducible curve singularities by their intersections with Schubert cells. Using their method, the author and his students proved that punctual Hilbert schemes of degree two for monomial plane curve singularities are isomorphic to a projective line. In this paper, we generalize this result for general monomial curve singularities.