Recent experiments on former facility FFTB at SLAC has demonstrated that a single electron beam driven Plasma Wakefield Accelerator (PWFA) can be produced with an accelerating gradient of 52 GeV/m over a meter-long scale*. If another electron bunch is properly loaded into such a wakefield, it will obtain a high energy gain in a short distance as well as a small energy spread. Such PWFA experiment with two bunches will be performed in FACET, which is a new facility at SLAC**. Simulation result s show that with possible beam parameters in FACET the first electron bunch (with less current than that in the FFTB experiment) can still produce a meter-long plasma column with a density of 5x10^{16} cm^{-3} via field ionization when we use a gas with a lower ionization energy. The second electron bunch can have a 10 GeV energy gain with a very narrow energy spread. If a pre-ionized plasma is used instead of the neutral gas, the energy gain of the second bunch can be enhanced to 30 GeV. Show Partial Abstract