We propose a carbon nanotube oscillator that is composed of a cantilever inner tube and a short outer tube. When the inner tube vibrates, the centrifugal force and the van der Waals force drive the outer tube to oscillate along the inner tube, which means that the oscillator can simultaneously output two frequencies. The operation frequencies of the oscillator may be tunable in a wide range (from tens of gigahertz to more than 100 GHz) by controlling the initial conditions. The combination of tunability and high-frequency operation makes the oscillators promising for a variety of scientific and technological applications. A continuum model is presented to study the frequency properties of the oscillator. The model is validated by the molecular dynamics simulations.