In order to solve the complex problem of concatenated GHZ(C-GHZ) state preparation, an improved scheme of C-GHZ state based on weak cross Kerr nonlinearity is proposed. Combining with the homodyne detection technology and the classical feedforward, the packaged optical element module and HWP22.5°half-wave plate are used to deduce the nm C-GHZ state from the simple C-GHZ state after repeated operation. Finally the preparation law of C-GHZ state is obtained. The required number of auxiliary single photons is nm, the number of modules is nm－1, and the number of HWP22.5° is n. The success rate simulation and feasibility analysis are conducted. Results show that increasing the amplitude intensity of coherent state |α〉 and reducing the loss of photon transmission can improve the success rate of C-GHZ state preparation.