The orthogonality between pulses of time-domain quadrature modulated signals of Prolate Spheroidal Wave Functions(PSWFs) is easily affected by channel characteristics.Among the channel compensation methods, the linear equalization method has limited compensation accuracy and the existing decision feedback equalization method has high training complexity for parallel signals. To solve these problems, a parallel adaptive decision feedback equalization method based on initialization parameter passing is proposed. The initialization parameter transfer method is used to realize the fast initialization of multiple parallel equalizers. The output weighted average mode conversion mechanism is used to quickly and accurately judge the switching time of decision-making mode.The simulation results show that the proposed method has fast convergence speed and low complexity, and the steady-state error is improved by 4 dB and 0.5 dB respectively compared with linear equalization method and traditional decision feedback equalization method.