The hybrid iterative angular spectrum method is an effective approach for computing holograms with reduced interlayer crosstalk noise. However, the use of a random phase as the initial phase results in speckle noise across all reconstructed planes. We propose a hybrid iterative angular spectrum method based on the double-phase amplitude encoding method. This method eliminates the constraints of the initial phase by employing a quadratic phase instead of a random phase as the initial phase, successfully reducing speckle noise in the reconstructed images. Through simulation and experimental validation, the algorithm demonstrates superior reconstruction performance, making it applicable to various fields such as biology, medicine, and engineering design. It provides a robust solution to the challenges of multi-plane image reconstruction.