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We propose to use HST-WFC3 in slitless grism mode to spectroscopically confirm the nature of eleven dual quasar candidates with projected separation between 0.35d_comma-0.7d_comma (corresponding to a projected separation of 3-6 kpc) comma an extremely rare population (11 out of 59 comma 025 quasars from a search area of 500 square degrees). With the exquisite wide and deep imaging from the Hyper Suprime-Cam Subaru Strategic Program comma we have identified a population of 386 SDSS quasars as having two bright and separate components that are candidates for dual supermassive black holes comma many of which are within the same host galaxy comma likely the result of a major merger. For eleven candidates that have the closest separation at z>1 comma HST is needed to spectroscopically confirm their nature and their redshift by detection of broad emission lines from both objects. The high sensitivity of HST would further help us to rule out the possibility of lensing. Any confirmed physical quasar pair from our candidates would be the first case ever confirmed that has a projected separation below 6 kpc beyond z>1. This sample will be the key to understanding the merger process and how it affects galaxy evolution and AGN activity comma since they are at close to final coalescence stage. Furthermore comma this program will provide remarkable laboratories for studying the fueling of dual supermassive black holes with ALMA study. Moreover comma taken together with the wider separation dual quasars confirmed by ground-based observations comma we will measure the dual quasar fraction and its evolution up to zvirgul3. The results will be compared with the predictions from recent hydrodynamic cosmological simulations.