Using the full potential linearized augmented plane wave (FLAPW) method, we have investigated the thickness dependent magnetic properties of rare earth free exchange spring magnet FeCo/FePt(001). The FeCo adlayer thickness is increased from one monolayer (ML) to four ML coverage. It is observed that the FeCo adlayers and Fe atoms in FePt substrate show almost half metallic behavior, while an ordinary metallic feature is found in Pt atoms. The average magnetization increases with FeCo thickness and the estimated maximum energy product reaches 66MGOe in FeCo(4ML)/FePt(001). A giant perpendicular magnetocrystalline anisotropy (MCA) energy of 18.20meV/cell is found in pure FePt(001) and it becomes 17.35meV/cell even in FeCo(4ML)/FePt(001). In addition, we find very large coercivity field in FeCo/FePt(001) systems. For instance, the calculated maximum coercivity field in FeCo(4ML)/FePt(001) is about 188kOe. Both energy product and coercivity field calculations may imply that the FeCo/FePt can be utilized for potential rare earth free exchange spring magnet material.