We present here a simple laser system for a laser cooled atom interferometer, where all functions (laser cooling, interferometry and detection) are realized using only two extended cavity laser diodes, amplified by a common tapered amplifier.One laser is locked by frequency modulation transfer spectroscopy, the other being phase locked with an offset frequency determined by an Field-Programmable Gate Array (FPGA) controlled Direct Digital Synthesizer (DDS), which allows for efficient and versatile tuning of the laser frequency. Raman lasers are obtained with a double pass acousto-optic modulator. We demonstrate a gravimeter using this laser system, with performances close to the state of the art.