As a classical problem of computational molecular biology, the multiple sequences alignment is also important foundational process. RNA is one of biological polymer, and is different from protein and DNA that the secondary structure of RNA is more conservative than its primary sequence. Therefore, RNA multiple sequences alignment require not only information of sequences, but also information of secondary structures which those sequences will form. Here, a program——QEA-MRNA, which based on quantum evolutionary algorithm(QEA) to align RNA sequences, is proposed. The program introduce a full crossover operator and a fitness function which considering the information of RNA premary sequence and secondary structure, and improving on prematurity controling and the convergent speed. The effectiveness and performance of QEA-MRNA are demonstrated by testing cases in BRAliBase.