The fundamental result of Paouris gives the large deviation estimate for Euclidean norms of log-concave vectors. We extend it to the case of l_r-norms and show that for r>=2, p>=1 the p-th moment of the l_r-norm of a log-concave random vector is comparable to the sum of the first moment and the weak p-th moment up to a constant proportional to r. Joint work with Marta Strzelecka (University of Warsaw).