Accurate values for the energy of the odd-parity J=0, 1, 2, 3 and 4 levels of neutral barium have been obtained using laser-atomic-beam spectroscopy. The Rydberg series 6snp3P0 (14<or=n<or=48), 6snp3P1 (15<or=n<or=48), 6snp3P2 (16<or=n<or=48), 6snp1P1 (15<or=n<or=48), 6snf3F2 (9<or=n<or=45), 6snf3F3 (10<or=n<or=45), 6snf3F4 (11<or=n<or=45), 6snf1F3 (10<or=n<or=45) as well as some 5d8p perturber levels have been observed. From the nearly unperturbed 6snp3P0 series are more accurate value of the first ionisation limit has been determined: I6s=42034.90+or-0.01 cm-1. The experimental data on the J=0, 2, 3 and 4 levels are interpreted by means of multichannel quantum defect theory.