Polarization is an intrinsic attribute of optical waves, so manipulating the polarization state of optical surface waves can be of a fundamental importance for the next-generation information and bio-photonics technology. Here, we show theoretically that the polarization of the Bloch surface wave (BSW) on a dielectric multilayer can be transformed between a transverse-electric (TE) state and a transverse-magnetic (TM) state by using the laterally continuous grooves inscribed on this multilayer. This polarization transformation can be enhanced or inhibited by the interference between the reflected BSW beams, which can be tuned by the periodicity and depth of the grooves. The maximum polarization transformation efficiency can be achieved as high as 43% when the number of grooves is increased to 10. A generalized Fresnel formula is proposed to describe the polarization transformation of the BSW beams. Due to this polarization transformation, an anomalous reflection of BSW beams can be realized, which is the inequality between the incident angle and the reflection angle.