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Observational evidences are accumulating that accretion discs around black holes can be warped.Warped accretion discs have been directly observed by wa ter maser observations in NGC4258 and Circinius galaxy.The lack of correlation of radio jets in AGNs and the disc plane of host galaxy can also be explained by disc warping.We consider a thin accretion disc warped due to the Bardeen-Petterson effect, presenting both analytical and numerical solutions for the situation in which the two viscosity coefficients vary with radius as a power law, with the two power-law indices not necessarily equal.The analytical solutions are compared with numerical ones, showing that our new analytical solution is more accurate than previous one, which overestimates the inclination changing in the outer disc.Our new analytical solution is appropriate for moderately warped discs, while for extremely misaligned disc only numerical solution is appropriate. The broad Balmer emission-line profiles resulting from the reprocessing of UV/X-ray radiation from a warped accretion disc induced by the Bardeen- Petterson effect are also studied.We adopt a thin warped disc geometry and a central ring-like illuminating source in our model.We compute the steady-state shape of the warped disc numerically, and then use it in the calculation of the line profile.We find that, from the outer radius to the inner radius of the disc,the warp is twisted by an angle～π before being flattened efficiently into the equatorial plane.The profiles obtained depend weakly on the illuminating source radius in the range from 3rg to 10rg, but depend strongly on this radius when it approaches the marginally stable orbit of an extreme Kerr black hole.Double-or triplet-peaked line profiles are present in most cases when the illuminating source radius is low.The triplet-peaked line profiles observed from the Sloan Digital Sky Survey may be a "signature" of a warped disc.