The extraordinary electronic structures of monolayer transition metal dichalcogenides, such as the spin-valley-coupled band edges, have sparked great interest for potential spintronic and valleytronic applications based on these two-dimensional materials. In this work, we report the experimental observation of quasi-particle interference patterns in monolayer WSe2 using low-temperature scanning tunnelling spectroscopy. We observe intervalley quantum interference involving the Q valleys in the conduction band due to spin-conserving scattering processes, while spin-flipping intervalley scattering is absent. Our results establish unequivocally the presence of spin-valley coupling and affirm the large spin splitting at the Q valleys. Importantly, the inefficient spin-flipping scattering implies long valley and spin lifetime in monolayer WSe2, which is a key figure of merit for valley-spintronic applications.