The 1T' phase of transition metal dichalcogenides (TMDs) with the form MX₂ (M = Mo, W; X = S, Se, Te) has been identified as a two-dimensional topological insulator, offering a promising platform for low-dissipation spintronic devices based on the quantum spin Hall effect. In this work, we demonstrate the successful growth of the 1T' phase WSe₂ on SrTiO₃ (001) substrates, instead of the thermodynamically more stable 2H phase. Using low-temperature scanning tunneling microscopy (STM), we observed robust edge states localized along the boundaries of 1T'-WSe₂ islands. Furthermore, quasiparticle interference (QPI) measurement, which probes the electronic band structure via scattering interference patterns, reveals a topological band dispersion consistent with angle-resolved photoemission spectroscopy (ARPES) results. Together, the observed edge states and QPI results establish the topologically nontrivial nature of 1T'-WSe₂.