This paper presents Hα emission line detections for four galaxies at z > 3.5 made with AKARI as part of the FUHYU mission program. These are the highest-redshift Hα detections to date in star-forming galaxies. AKARI's unique near-infrared spectroscopic capability has made these detections possible. For two of these galaxies, this represents the first evidence of their redshifts and confirms their physical association with a companion radio galaxy. The star formation rates (SFRs) estimated from the Hα lines under-predict the SFRs estimated from their far-infrared luminosities by a factor of ~ 2 - 3. We have also detected broad Hα components in the two radio galaxies which indicate the presence of quasars.