Galaxy clusters provide an excellent probe in various research fields in astrophysics and cosmology. However, the number of galaxy clusters detected so far in the AKARI North Ecliptic Pole (NEP) field is limited. In this work, we provide galaxy cluster candidates in the AKARI NEP field with the minimum requisites based only on the coordinates and photometric redshift (photo-z) of galaxies. We used galaxies detected in five optical bands (g, r, i, z, and Y) by the Subaru Hyper Suprime-Cam (HSC), with additional data from the u band obtained from the Canada-France-Hawaii Telescope (CFHT) MegaPrime/MegaCam, and from the IRAC1 and IRAC2 bands from the Spitzer space telescope for photo-z estimation. We calculated the local density around every galaxy using the 10th-nearest neighbourhood. Cluster candidates were determined by applying the friends-of-friends algorithm to over-densities. A total of 88 cluster candidates containing 4390 member galaxies below redshift 1.1 in 5.4 deg(2) were identified. The reliability of our method was examined through false-detection tests, redshift-uncertainty tests, and applications on the Cosmic Evolution Survey (COSMOS) data, giving false-detection rates of 0.01 to 0.05 and a recovery rate of 0.9 at high richness. Three X-ray clusters previously observed by ROSAT and Chandra were recovered. The cluster galaxies show a higher stellar mass and lower star formation rate compared with the field galaxies in two-sample Z-tests. These cluster candidates are useful for environmental studies of galaxy evolution and future astronomical surveys in the NEP, where AKARI has performed unique nine-band mid-infrared photometry for tens of thousands of galaxies.