A quantum spin hall insulator is manifested by its conducting edge channels that originate from the nontrivial topology of the insulating bulk states. Monolayer 1T^{'}-WTe_{2} exhibits this quantized edge conductance in transport measurements, but because of its semimetallic nature, the coherence length is restricted to around 100 nm. To overcome this restriction, we propose a strain engineering technique to tune the electronic structure, where either a compressive strain along the a axis or a tensile strain along the b axis can drive 1T^{'}-WTe_{2} into an full gap insulating phase. A combined study of molecular beam epitaxy and in situ scanning tunneling microscopy or spectroscopy then confirmed such a phase transition. Meanwhile, the topological edge states were found to be very robust in the presence of strain.