The design of a two-stage compact GeV electron accelerator is presented. The accelerator is as follows: (1) an ultra-short electron bunch is produced in a state-of-the-art laser-plasma accelerator (injector stage), (2) it is injected into an accelerating stage consisting of a centimeter length low density plasma interacting with a petawatt laser pulse. The parameters for the injector are taken from recent experimental results showing that high quality, ultra-short, and quasi-monoenergetic electron beams are now being produced in laser-plasma accelerators. Simulations performed with WAKE show that this method can lead to the production of high quality, monoenergetic, and sub-50 fs electron bunches at the GeV energy level.