Based on all the tRNA sequences with high similarity in their functions and structures, 3420 tRNA sequences are put as a whole in this paper, and then the palindromic sequences of different length within all the tRNA sequences are counted. We observed that: (I) the probability of one given palindromic sequence P(i) with the given palindromic sequence i follows a power-law distribution when the length of the palindromic sequences is between five and fifteen bases, and in this case, the total number N(n) of palindromic sequences which occur n times with the occurrences n follows a power-law distribution too; (II) the repeated palindromic sequences are found nearly at the same site in the different tRNA sequences as their length is longer than five bases; In addition, the longer palindromic sequences are always discovered in the center or both sides of some stem-loops of tRNA sequences; (III) the palindromic sequences of absolute AT/GC content almost decrease with the increase of the length of palindromic sequences K, and the palindromic sequences of absolute AT content are always more than the GC content for a same K value. By the analysis of the palindromic sequences among all the tRNA sequences, the structure and evolution process of tRNA sequences are also discussed in this paper.