A palindrome is a string of the form S = A1 A2 or S = A1 aA2, where A1 and A2 are substrings of S and the reverse of A2 exactly matches with A1. DNA palindromes show direct influence on tumerogenesis due to the formation of DNA palindromes at microRNA genes, which involve in tumor development. Furthermore, RNA palindromes play a crucial role in genomic instability and gene amplification in some human cancers. Therefore, it is important to develop effective approaches to identify and characterize biological approximate palindromes. In this paper, we developed a simple algorithm to find all the exact and approximate palindromes up to k errors (k is specified by the user) for the two different types of RNA sequence data, i.e. mRNA sequences of fusion genes and human microRNAs (miRNAs). We confirmed that the palindromes in RNA sequences are A-U rich. According to the Kolmogorov-Smirnov test, it was found that miRNA has a frequency distribution of palindromes different from the fusion genes' mRNAs. The proposed algorithm is easy to implement, which provides an effective tool for investigating the relationship between palindromes and cancer biology.