We propose a new model which can simultaneously and naturally explain the origins of fermion generation, quark mass hierarchy, and the Cabibbo-Kobayashi-Maskawa matrix from the geometry of an extra dimension.We take the extra dimension to be an interval with point interactions, which are additional boundary points in the bulk space of the interval. Because of the Dirichlet boundary condition for fermions at the positions of point interactions, profiles of chiral fermion zero modes are split and localized, and then we can realize three generations from each five-dimensional Dirac fermion. Our model allows fermion flavor mixing but the form of the non-diagonal elements of fermion mass matrices is found to be severely restricted due to the geometry of the extra dimension. The Robin boundary condition for a scalar leads to an extra coordinate-dependent vacuum expectation value, which can naturally explain the fermion mass hierarchy. © The Author(s) 2013.