In this paper, using an angular spectrum method, we develop an analytical theory for Airy surface plasmon wave excited in a classical Kretschmann setup. It is found that the center of an Airy surface plasmon polariton (SPP) wave has a giant positive lateral shift, and the sidelobes move forward along the surface. The intensity of the Airy SPP wave is greatly enhanced, the corresponding optical forces can be enhanced by more than one order of magnitude. Importantly, we show that the sidelobes of the Airy SPP beam can lead to the splitting of optical force spectra with the variation of incident angle, which is accompanied by strong oscillations emerging at the optimal metal layer thickness. Moreover, the effects of multiple scatterings of the Airy SPP wave between the particle and the metal layer are also discussed. The theoretical analysis could open up new perspectives for the applications of Airy beam in optical manipulation and surface-enhanced Raman scattering.