The characteristics of the guided electromagnetic wave propagation through a subwavelength hole surrounded by a doubly dispersive metamaterial are investigated. Characteristic equations are derived for the surface polariton modes related to the subwavelength hole and mode classifications established. The surface polariton modes for two different hole-radii are numerically obtained and their electromagnetic dispersion curves and power flux characteristics analyzed and compared with each other. In particular, it was found that the border of the counter-propagation between the forward and backward Poynting vectors was located within the metamaterial, rather than at the interface between the metamaterial and the free space.