The contribution of carrier tunneling and gate induced drain leakage (GIDL) effects in the total gate and drain currents of FinFET devices with different dimensions is analyzed. In order to fulfill this task, expressions for the leakage current due to carrier tunneling and GIDL effects at a Metal-Dielectric-Semiconductor structure were established and incorporated in the Symmetric Doped Double-Gate Model (SDDGM) for metal-oxide-semiconductor field-effect transistors (MOSFET). It is shown that both phenomena have to be taken into account for precise modeling of the device in all the operation regions although GIDL current can become predominant in the subthreshold region. The dependence of gate tunneling current in inversion and subthreshold regimes of operation is modeled as function of the applied voltages and transistor physical parameters by using analytical expressions. The present leakage current model is validated by comparing modeled with measured total gate and drain currents for FinFETs with different dimensions.