The　growth　rate　of　the　out-of-time-ordered　correlator　in　a　N-flavor　Fermi　gas　is　investigated　and　the　Lyapunov　exponent　lambda(L)　is　calculated　to　the　order　of　1/N.　We　find　that　the　Lyapunov　exponent　monotonically　increases　as　the　interaction　strength　increases　from　the　BCS　limit　to　the　unitary　region.　At　the　unitarity,　the　Lyapunov　exponent　increases　while　the　temperature　drops　and　it　can　reach　to　the　order　of　lambda(L)similar　to　T　around　the　critical　temperature　for　the　N　=　1　case.　For　N　-＞　infinity,　the　Lyapunov　exponent　reaches　its　maximum　lambda(L)　approximate　to　4.35T/N　at　the　critical　temperature.　The　system　scrambles　faster　for　stronger　pairing　fluctuations.　At　the　BCS　limit,　the　Lyapunov　exponent　behaviors　as　lambda(L)　proportional　to　e(mu/T)a(s)(2)T(2)/N.