Carbon nanotubes (CNTs) have emerged as promising candidates for nanoscale field effect transistors. The contact between metal and CNT can be of Ohmic or Schottky type. Schottky contact CNTFETs operate by modulating the transmission coefficient of the Schottky barriers at the contact between the metal and the CNT, but the ambipolar behavior of Schottky barrier CNTFETs limits the performance of these devices. We show that by using a double gate structure the ambipolar behavior of these devices can be suppressed. For simplicity we considered a coaxial geometry where the gate covers all around the CNT. Assuming ballistic transport, we used a Schrodinger-Poisson solver for the analysis of Schottky barrier CNTFETs. In this work we focus on ambipolar devices, where the metal Fermi level is located in the middle of the CNT band gap at each contact. All our calculations assume a CNT with 0.6 eV band gap, corresponding to a diameter of 1.4 nm.