For the semicircular plasmonic lens, the spiral phase is the origin of the spin-dependent surface plasmon polariton (SPP) focusing. By counterbalancing the spin-dependent spiral phase with another spiral phase or Pancharatnam-Berry phase, we realized the SPP focusing independent from the spin states of the excitation light. Analyses based on both Huygens-Fresnel principle for SPPs and numerical simulations prove that the position, intensity, and profile of the SPP focuses are exactly the same for different spin states. Moreover, the spin-independent SPP focusing is immune from the change of the radius, the central angle, and the shape of the semicircular slit. This study not only further reveals the mechanism of spin-dependent SPP devices but also provides effective approaches to overcome the influence of spin states on the SPPs field.