Monolayer 1T'-WTe₂ has exhibited clear quantized transportation originated from the quantum spin Hall phase, while the channel length with quantized conductance is restricted around 100 nm due to its semimatellic nature. To overcome this problem, it is crucial to find a way to engineer the electronic structure. Through a combined in-situ scanning tunneling microscopy/spectroscopy (STM/STS) and Density functional theory (DFT) study, we demonstrate that strain can effectively manipulate the band structure of monolayer 1T'-WTe₂ to realize a phase transition from a semimetal to an insulator upon application of a compressive strain along a axis or a tensile strain along b axis. Moreover, the topological edge states are found to be very robust against strains. Besides, we find that the out-of-plane distortions can also significantly change the band structure. Our results reveal the clear strain dependence of electronic properties and phases of monolayer 1T'-WTe₂, which provides an effective approach to realize the long-coherent quantized conductance for the further transport experiments verification.