In iron-pnictide superconductivity, the interband interaction between the hole and electron Fermi surfaces (FSs) is believed to play an important role. However, KFe(2)As(2) has three zone-centered hole FSs and no electron FS but still exhibits superconductivity. Our ultrahigh-resolution laser angle-resolved photoemission spectroscopy unveils that KFe(2)As(2) is a nodal s-wave superconductor with highly unusual FS-selective multi-gap structure: a nodeless gap on the inner FS, an unconventional gap with "octet-line nodes" on the middle FS, and an almost-zero gap on the outer FS. This gap structure may arise from the frustration between competing pairing interactions on the hole FSs causing the eightfold sign reversal. Our results suggest that the A(1g) superconducting symmetry is universal in iron-pnictides, in spite of the variety of gap functions.