Electric polarizabilities of four low-J even-parity states and three low-J odd-parity states of atomic barium ranging from 35, 600 to 36, 000 cm −1 are investigated. The states of interest are excited (in an atomic beam) via an intermediate odd-parity state with a sequence of two laser pulses. The odd-parity states can be excited due to the Stark-induced mixing with even-parity states. The polarizabilities are measured via direct spectroscopy on the second-stage transition.Several states have tensor and scalar polarizabilities that exceed the values that might be expected from the known energy levels of barium by more than two orders of magnitude. Two of the Stark-induced transitions cannot be identified from the known energy spectrum of barium. The observations suggest the existence of as yet unidentified odd-parity energy states, whose energies and angular momenta are determined in the present experiment. A tentative identification of these states as [Xe]6s8p 3 P 0,2 is suggested.