Neutron activation cross sections between 15 and 40 MeV were measured by the activation method using a monoenergetic neutron field based on the 7Li(p,n)7Be reaction. Natural samples of carbon and cobalt, and separated isotope samples of 30Si, 47Ti, 48Ti, 52Cr and 58Ni were irradiated in the p-Li neutron fields generated by 20, 25, 30, 35, and 40 MeV protons. Neutron yields were determined from the amount of 7Be induced in the lithium target. The amount of 7Be was measured by observing the 0.478-MeV gamma rays of 7Be(T1/2 = 53.29 days) after the irradiation experiment. Cross sections of 12C(n,2n)11C, 30Si(n,np)29Al, 47Ti(n,np)46m+gSc, 48Ti(n,np)47Sc, 52Cr(n,2n)51Cr, 59Co(n,2n)58m+gCo, 59Co(n,3n)57Co, 59Co(n,4n)56Co, and 58Ni(n,2n)57Ni are reported.