Neutron-production double-differential cross sections for 870-MeV π+ and π - and 2.1-GeV π+ mesons incident on iron and lead targets were measured with NE213 liquid scintillators by time-of-flight technique. NE213 liquid scintillators 12.7cm in diameter and 12.7cm thick were placed in directions of 15°, 30°, 60°, 90°, 120° and 150°. The typical flight path length was 1.5 m. Neutron detection efficiencies were derived from the calculation results of SCINFUL and CECIL codes. The experimental results were compared with the cascade-evaporation calculation code NUCLEUS. The calculation results are higher typically by a factor of two than the experimental data at neutron energies below about 30MeV. NUCLEUS overestimates π+-incident neutron-production cross sections in forward angles at neutron energies of 100 to 500 MeV.