We present the electric properties of p-InAs nanowire field-effect transistors showing ambipolar conduction. Be doped nanowires are grown by the vapor-solid-solid mechanism using molecular beam epitaxy with in situ deposited Au catalyst particles. P-type conduction in InAs nanowires is challenging because of the Fermi-level pinning above the conduction band edge at the nanowire surface that leads to creation of an electron inversion layer. We demonstrate that this task is possible without a modified surface and report a strong temperature dependence (10–105) of the on-off ratio caused by the surface inversion layer.