A Rutherford-type cable is one of candidate conductors for a large-scale or high-field superconducting magnet. It is important to evaluate the internal strain state of strand consisting of a cabling conductor to understand the strain dependence of superconducting properties. Internal lattice strains under a tensile load for Nb-rod-processed Nb3Sn Rutherford cable with and without the prebending treatment were measured directly by neutron diffraction at room and low temperatures. Stress-lattice strain curves of Nb3Sn were obtained, and it was found that the internal lattice strain is smaller than the strain measured on the cable surface by an extensometer above 100 to 150 MPa. It is important to evaluate not only the strain on the cable surface but also the internal strain of a strand in cabling conductors.