Non-symmorphic crystals are generating great interest as they are commonly found in quantum materials, like iron-based superconductors, heavy-fermion compounds, and topological semimetals. A new type of surface state, a floating band, was recently discovered in the nodal-line semimetal ZrSiSe, but also exists in many non-symmorphic crystals. Little is known about its physical properties. Here, we employ scanning tunneling microscopy to measure the quasiparticle interference of the floating band state on ZrSiSe (001) surface and discover rotational symmetry breaking interference, healing effect and half-missing-type anomalous Umklapp scattering. Using simulation and theoretical analysis we establish that the phenomena are characteristic properties of a floating band surface state. Moreover, we uncover that the half-missing Umklapp process is derived from the glide mirror symmetry, thus identify a non-symmorphic effect on quasiparticle interferences. Our results may pave a way towards potential new applications of nanoelectronics.