The paper is concerned with the standard \(L^p\) estimate of solutions to the resolvent problem for the Stokes operator on an infinite layer with “Neumann-Dirichlet-type” boundary condition. Using the same approach as in former papers of the author and and Y. Shibata the aim of this paper is to obtain the resolvent estimate so that the constant in it does not depend on the resolvent parameter \(\lambda\). The main result asserts that \(\lambda=0\) belongs to the resolvent set of the Stokes operator on an infinite layer domain with “Neumann-Dirichlet type boundary condition. Since \(\lambda=0\) does not belong to the resolvent set of the Stokes operator on unbounded domains generally, this is one of the oustanding features of the problem.