Stark splitting of the barium 6snp P states with principal quantum numbers ranging from 8 to 15 and of the 5d7p P perturber level was measured in an atomic beam via pulsed laser excitation with timeand wave length-resolved fluorescence detection at low electric field strengths. Tensor polarizabilities were derived from the quantum beat signals observed in pure homogeneous electric fields. Strong variations of the tensor polarizabilities of the levels in the 6snp P series were found.