We theoretically investigate the control of surface plasmon polariton (SPP) generated at the interface of dielectric and graphene due to effective variation of dielectric functions. The input light pulse is controlled and modified in a Doppler broadening dielectric medium. The controlled and modified output, from Doppler broadening dielectric medium is used to excite SPPs at the interface of graphene and dielectric medium. It is noted that at high Doppler width the absorption/dispersion and propagation length of SPPs become saturated and significantly affected by strength of the control fields. The inverse Doppler effect enhances the group speed of SPPs but suddenly decreases at the region of SPPs hole burning. These results have potential applications in optical tweezers, nano-photonics, radiations guiding, plasmonster technology, photovoltaic devices, data storage devices, biosensor technology and solar cells.