The Computer Generated Hologram of Gyrator Transform (GT-CGH) is proposed based on the numerical algorithm of gyrator transform (GT) and the theory of Computer Generated Hologram (CGH). The Lohmann coding method is applied to produce the GT-CGHs at different transform angles. Their digital reconstructions are also realized respectively. The rules of reconstructions are consistent with the GT hologram reported in the relevant paper, which shows that it is feasible to create the GT-CGH. A novel encoding method, encoding by equivalent area of trapezium, is proposed for the CGH. This method can be effective to increase the phase quantization order in a single sampling unit.The simulation experiments of the creation and digital reconstruction are performed on CGH of Fourier Transform (FT-CGH) with the new encoding method. The results show that the reconstruction of the off-axis CGH at the 0th order diffraction can be realized by the application of new method. By using the new method, the production and the digital reconstruction of GT-CGH are also realized. The experimental results above all demonstrate the feasibility and validity of the proposed new type encoding method for the CGH.