Given any non-abelian finite simple group G and any generating set S, it is conjectured by Laszlo Babai that its Cayley graph should always have diameter (log|G|)^O(1). This conjecture has been verified for all finite simple groups of Lie type with bounded rank, but little progress has been made in the cases with large rank. Motivated by the methods of Babai and Seress for symmetric groups, we obtained an improved diameter bound of q^O(n(log n + log q)^3) for finite simple groups of Lie type with large rank.  Joint work with Arindam Biswas from University of Paris-Sud.