ULTIMATE-Subaru (Ultra-wide Laser Tomographic Imager and MOS with AO for Transcendent Exploration on Subaru) and WFIRST (Wide Field Infra-Red Survey Telescope) are the next generation near-infrared instruments that have a large field-of-view. They allow us to conduct deep and wide transient surveys in near-infrared. Such a near-infrared transient survey enables us to find very distant supernovae that are redshifted to the near-infrared wavelengths. We have performed the mock transient surveys with ULTIMATE-Subaru and WFIRST to investigate their ability to discover Population III pair-instability supernovae. We found that a 5-year 1 deg2 K-band transient survey with the point-source limiting magnitude of 26.5 mag with ULTIMATE-Subaru may find about 2 Population III pair-instability supernovae beyond the redshift of 6. A 5-year 10 deg2 survey with WFIRST reaching 26.5 mag in the F184 band may find about 7 Population III pair-instability supernovae beyond the redshift of 6. We also find that the expected numbers of the Population III pair-instability supernova detections increase about a factor of 2 if the near-infrared transient surveys are performed towards clusters of galaxies. Other supernovae such as Population II pair-instability supernovae would also be detected in the same survey. This study demonstrates that the future wide-field near-infrared instruments allow us to investigate the explosions of the first generation supernovae by performing the deep and wide near-infrared transient surveys.