Topological state of matter remains one of the central topics in condensed matter physics since decades ago. Take graphene as an example, the electron bands are linear and touching with each other in the Brillouin zone. The dispersion near these touching points can be described by the Dirac equation, therefore the excited massless quasiparticles and these touching points are called Dirac electrons and Dirac points, respectively. Analogous to the linear band touching of electrons, recently a spin web compound Cu3TeO6 (CTO) has been proposed to support the Dirac magnon excitations near the linear band touching points of the optical magnon branches. Hence, mapping out the spin excitation spectra in the bulk to check whether there are linear band touching points directly is critical to test the idea of the formation of Dirac magnon bands in CTO.