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Given any non‐abelian finite simple group   G   and any generating set   S  , it is conjectured by László Babai that the diameter of the Cayley graph is bounded by(  log  |  G  |  )    O  (  1  )    . This conjecture has been verified for all finite simple groups of Lie type with bounded ranks, but little progress has been made in cases with large ranks. Motivated by the methods of Babai and Seress for symmetric groups, we obtained an improved diameter bounds for finite simple groups of Lie type with large rank. If the finite simple group   G   is an algebraic group of rank   n   over the field of order   q  , its diameter is bounded by    q   O  (  n    (  log  n  +  log  q  )   3   )    . In particular, if   q   is bounded, then this diameter bound would be    q   O  (  n    (  log  n  )   3   )    .

A diameter bound for finite simple groups of large rank