The successive phase transitions of multiferroic barium sodium niobate, Ba2NaNb5O15 (BNN), were studied by Brillouin scattering. The LA, TA modes, and central peak were measured in a large temperature range from room temperature up to 750 degrees C. In the vicinity of a ferroelectric phase transition at about T-C = 585 degrees C from the prototypic tetragonal 4/mmm to ferroelectric 4mm phases, elastic anomaly was observed for LA and TA modes. In addition, the order-disorder nature was observed by the temperature dependence of a central peak. For further cooling another elastic anomaly was also observed in the vicinity of a ferroelastic incommensurate phase transition at about T-IC = 285 degrees C into orthorhombic 2mm phase with the appearance of incommensurate modulation. The large thermal hysteresis of elastic anomaly near T-IC can be attributed the typical feature of the type III incommensurate phase transition predicted recently by Ishibashi and Iwata (2013 J. Phys. Soc. Jpn. 82 044703).