Abstract: The closed-loop surface-related multiple elimination (CL-SRME) method shares a common theoretical foundation with the traditional surface-related multiple elimination (SRME) approach. Unlike SRME using adaptive subtraction, CL-SRME directly estimates primary waves through waveform inversion for effective multiple suppression, which avoids potential primary energy loss caused by primary-multiple interference during suppression and enables precise multiple attenuation while effectively preserving primary energy. As a waveform inversion-based method, the convergence rate of primary-wave estimation is a key factor affecting CL-SRME performance. Therefore, a (Polak-Ribière-Polyak-Fletcher-Reeves)PRP-FR hybrid conjugate gradient method is introduced to accelerate the convergence of the inversion process, thereby achieving more accurate primary-wave estimation with fewer iterations. Synthetic and field data tests demonstrate the effectiveness and adaptability of the proposed method.