The solutions of a boundary problem with non-local boundary conditions for a three-dimensional Laplace equation are studied. Here, the boundary conditions are the most common and linear. Further, we note that the singular integrals appearing in the necessary conditions are multi-dimensional. Therefore, the regularization of these singularities is much more difficult than the regularization of one-dimensional singular integrals. After the regularization of singularities the Fredholm property of the problem is proved.