A numerical method based on cut-cell method was extended for turbulent flows in this study. Computational studies with modeling near wall boundary layer have emerged as the one of practical method in the industries. Most of merits of the method is due to a serious reduction of computational costs. A cut-cell method can obtain better spatial resolution because: (1) an obliquity of walls are captured and (2) conservations of mass and momentum are easier of attainment for each cross section. Conventional cut-cell methods focused on flux control across on the computational cells. In a proposed method, we changed the calculation procedure of stress tensor directly by using the distance from wall and velocity information. This extension made easy use of wall laws for laminar and turbulent boundary layers. The function can be selected from some proposed wall function model. In this study, the following two model were used: non-slip wall model and Allmaras wall model. As a result, the law of the wall model can be effectively incorporated on the Cartesian grid with high engineering applicability. In addition, higher efficient algorithm for orthogonal structured grid can be applied without serious reconstruction of programming source code. To demonstrate the method, (1) two-dimensional laminar flow in an inclined channel, (2) flow around a cylinder, and (3) turbulent flows over a wall-mounted hump were calculated. As a result of applications, the proposed method could easily take into account the flows with distorted boundary walls.