The gate induced drain leakage (GIDL) effect in negative capacitance (NC) FinFET is investigated. A Landau-Ginzburg-Devonshire equation (which considers the polarization gradient in ferroelectric material) is used to estimate the characteristics of the NC FinFET. Specifically, metal-ferroelectric-metal-insulator-semiconductor (MFMIS) and metal-ferroelectric-insulator-semiconductor (MFIS) NC FinFETs are compared, in order to figure out the effect of the internal metal layer on the GIDL effect. To analyze the impact of the polarization gradient on the GIDL effect in NC FinFET, a polarization gradient coefficient is varied. For MFMIS, the polarization gradient doesn't significantly affect the device performance. The subthreshold swing improves but the GIDL effect deteriorates because of the "uniform" NC effect in channel region. For MFIS, the device performance is explicitly affected by the polarization gradient. Smaller polarization gradients result in non-uniform NC effect in channel region, resulting in severe GIDL effects. On the other hand, higher polarization gradients alleviate GIDL effects.