We propose three-terminal core-shell (CS) silicon vertical nanowire tunneling field-effect transistors (TFETs), which can be fabricated by conventional CMOS technology. CS TFETs show lower subthreshold swing (SS) and higher on-state current than conventional TFETs through their high surface-to-volume ratio, which increases carrier-tunneling region with no additional device area. The on-state current can be enhanced by increasing the nanowire height, decreasing equivalent oxide thickness (EOT) or creating a nanowire array. The off-state current is also manageable for power saving through selective epitaxial growth at the top-side nanowire region. CS TFETs with an EOT of 0.8 nm and an aspect ratio of 20 for the core nanowire region provide the largest drain current ranges with point SS values below 60 mV/dec and superior on/off current ratio under all operation voltages of 0.5, 0.7, and 1.0 V. These devices are promising for low-power applications at low fabrication cost and high device density.