Transcendental　logarithm　problem　is　a　new　problem　which　can　be　used　to　build　signature　schemes.　Although　no　polynomial　time　algorithm　or　sub-exponential　time　algorithm　has　been　found　to　solve　this　problem,　whether　it　is　still　an　intractable　problem　with　quantum　computers　is　a　question.　In　this　paper,　we　solve　the　transcendental　logarithm　problem　with　improved　Grover＇s　quantum　search　algorithm.　In　allusion　to　some　characteristics　of　the　transcendental　logarithm　problem,　the　average　number　of　the　Grover　iterations　can　be　reduced　to　lower　the　time　complexity.　The　algorithm　calls　the　oracle　operator　fewer　times　than　before.　According　to　our　theoretic　analysis　and　simulation　data,　cryptosystems　based　on　transcendental　logarithm　problem　can　be　improved　through　increasing　the　length　of　the　key　or　modifying　the　original　problem　by　adding　suitable　parameters　to　lower　the　number　of　solutions.