We numerically study the surface plasmon interference formed by tightly focused higher polarization order axially symmetric polarized beams (ASPBs) based on the vectorial diffraction theory. The definition of ASPBs is stated, and the optical setup for surface plasmon polariton (SPP) excitation and mathematical expressions for interfering SPP fields are proposed. The simulation results show that the interfering SPP fields present a multi-focal spot pattern. In addition, the number of spots is related to the polarization order of the incident beams P as 2\times(P-1), indicating potential utilization in near-field multiple optical trapping and near-field imaging and sensing. The unique interfering phenomenon is also explained.