To　enhance　the　scalability　and　performance　of　the　traditional　finite-difference　time-domain　(FDTD)　methods,　a　3-D　summation-by-part　simultaneous　approximation　term　(SBP-SAT)　FDTD　method　is　developed　to　solve　complex　electromagnetic　problems.　It　is　theoretically　stable　and　can　be　further　used　for　multiple　mesh　blocks　with　different　mesh　sizes.　This　article　mainly　focuses　on　the　fundamental　theoretical　aspects　upon　its　3-D　implementation,　the　SAT　for　various　boundary　conditions,　and　the　numerical　dispersion　properties　and　the　comparison　with　the　FDTD　method.　The　proposed　SBP-SAT　FDTD　method　inherits　all　the　merits　of　the　FDTD　method,　which　is　matrix-free,　easy　to　implement,　and　has　the　same　level　of　accuracy　with　a　negligible　overhead　of　runtime　and　memory　usage.　Four　numerical　examples　are　carried　out　to　validate　the　effectiveness　of　the　proposed　method.