Experimental data have been obtained on the neutron elastic scattering cross sections for 55, 65 and 75 MeV neutrons, and non-elastic scattering cross sections for 40 to 80 MeV neutrons using the $^7Li(p,n)$ neutron source at TIARA of Japan Atomic Energy Research Institute and the TOF method. Data were obtained for C, Si, Fe, Zr, and Pb of natural elements. Elastic scattering data were obtained for 25 laboratory angles between 2.6 and 53.0 that clarified the angular distributions and angle integrated values. The data obtained were compared favorably with recent LA150 data library.