The ability of spoof surface plasmon polaritons (SSPPs) to confine electromagnetic fields in a subwavelength regime enables the design of miniaturized antennas. However, the impedance matching scheme for miniaturized spoof plasmonic antennas has not been studied systematically. In this paper, we propose a general method in the antenna design based on SSPPs, providing a feasible solution to impedance matching at the feeding point of miniaturized spoof plasmonic antennas. To verify the method, a prototype of a planar spoof plasmonic dipole antenna is simulated, fabricated and measured, of which the dipole arm length is reduced by 35.2% as compared with the traditional dipole antenna. A peak gain level of 4.29 dBi and the radiation efficiency of about 94.5% were measured at 6 GHz. This general method can be extended to solve the impedance matching problem in the design of other spoof plasmonic devices.