The structural, electronic and magnetic properties of the hexagonal nanolaminated layered MAX phases compound Cr2GeC are investigated using the full-potential linearized augmented-plane-waves (FPLAPW) method within the generalized gradient approximation (GGA) and GGA+U calculations. The results indicate Cr2GeC has a sizable moment of 1.667 渭B revealing the existence of a ferrimagnetic ground state in a MAX phase compound. This surprising new result will lead to the possibility of applying the layered magnetic MAX phase compounds in electronics and spintronics areas.