To apply the direct numerical simulation(DNS) and the large-eddy simulation(LES) of turbulence to flow fields of complicated geometry, a higher-order finite-difference method(FDM) has been developed for the body-fitted coordinate system. The consistency and the conservation property of FDMs are discussed for the collocated grid. As numerical examples, DNS results of decaying isotropic turbulence and DNS / LES results for plane channel flow are shown and the influence of variable arrangement is examined. The results by the consistent 'interpolation'method for gradient from on the collocated grid agree well with those by other proper FDMs and the spectral method.