Owing to their unique optical properties and new degrees of freedom, orbital angular momentum (OAM) beams have been applied in various fields. Detection of the topological charges (TCs) of OAM beams is the key step for their applications. However, on-chip sorting of OAM beams with large TCs still remains a challenge. In this paper, Bloch surface wave (BSW) structures with five semi-ring shaped nanoslits are modeled. A spatial separation of 135 nm on the chip is obtained between two neighboring OAM states. OAM beams with TCs up to 35 can be successfully sorted by the BSW structures, which is much larger than that using metallic structures (only seven). BSW structures exhibit better OAM sorting performances than metallic structures. We systematically show how the lower attenuation of BSW structures leads to far superior separation ability compared to surface plasmons propagating on metallic structures. In addition, sorting of two OAM beams with different TCs simultaneously can be achieved in this way. Our results reveal that BSW structures should be an excellent solution for OAM sorting with large TCs, which is beneficial for applications in integrated on-chip devices and optical communications.