Surface plasmon polaritons, sometimes referred to as Surface Plasmons (SPs) have brought us great opportunities to work in nanoscale at optical frequencies. The SPs at the two surfaces of a thin metal film interact with each other, hence generate new modes which are either symmetric or anti-symmetric. For anti-symmetric modes, the dispersion curve turns to be of negative slope at large wave vectors, so two different anti-symmetric modes can be excited at the same frequency. These two modes can form beats with novel features. The envelope (profile) of the beating SP waves could be stationary, which means its shape will not change in time. Our simulation results clearly showed such phenomena, which is a strong evidence of the SPs dispersion relations at the thin metal film. It is a proof of the existence of negative group velocity of SPs. Beats can help us determine the difference in k and the amplitudes ratio of the two beating waves. We also studied beating between anti-symmetric mode and symmetric mode SPs with the same frequency. The study of the energy density distribution showed that the output from such system can be well controlled through beats formation. Example by using NSOM (Near-field Scanning Optical Microscopy) has been simulated. The beating phenomena have a potential application in the integrated optical circuits.