We generalise the rank-level duality (also known as strange duality) proved by P. Belkale [J. Amer. Math. Soc. 21 (2008), no. 1, 235–258] for generic curves and A. Marian and D. Oprea [Invent. Math. 168 (2007), no. 2, 225–247] for every smooth curve to the case of spaces of conformal blocks related to moduli spaces of parabolic bundles on a smooth pointed projective curve.