In this paper, we study the itinerant ferromagnetic phase in multi-component fermionic systems with symplectic (Sp(4), or isomorphically SO(5)) symmetry. Two different microscopic models have been considered and an effective field theory has been proposed to study the critical behavior of the nonmagnetism-magnetism phase transition. It has been shown that such systems exhibit intriguing ferromagnetism and critical behavior that different from those in spin-$frac 12$ fermionic systems, or in high-spin systems with SU(N) symmetry. An extension of our results to higher spin systems with Sp(2N) symmetry has also been discussed.
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