Abstract. In 2007, Z. Huang showed that in the thick part of the moduli space M g of compact Riemann surfaces of genus g, the sectional curvature of the Weil-Petersson metric is bounded below by a constant depending on the injectivity radius, but independent of the genus g. In this article, we prove this result by a different method. We also show that the same result holds for Ricci curvature. For the universal Teichmüller space equipped with a Hilbert structure induced by the Weil-Petersson metric, we prove that its sectional curvature is bounded below by a universal constant.