Cross sections of natZr(n,xn)88Zr and natZr(n,xn)89Zr were measured at six neutron energies in the energy range of 29.4–42 MeV by irradiating natural zirconium (natZr) samples. The neutrons were produced via 9Be(p,n)9B reaction induced by bombarding a 0.25 mm thick beryllium target with 35, 40, and 45 MeV protons. The neutron spectrum produced at each proton energy was simulated by using the PHITS code. Two neutron peaks were observed in the simulated spectra for each proton energy. By using the estimated activity ratio factor for each neutron peak and experimentally measured γ-ray activities of 89Zr and 88Zr, the cross sections of natZr(n,xn)89Zr and natZr(n,xn)88Zr reactions were obtained, respectively. These experimentally measured cross sections were compared with the cross sections estimated by the TALYS-1.95 calculations and those from the EAF library. For natural zirconium, these cross sections are reported here for the first time in the neutron energy range of 29.4–42 MeV.