The nonlinear surface plasmon polariton (SPP) supported by a linear/metal-nonlinear slab waveguide was studied analytically. The dispersion conditions were obtained from fundamental Maxwell’s equations to determine the propagation characteristics of the nonlinear SPPs supported by the waveguide. The mode profile of the nonlinear mode was studied to analyze the physics behind the observed propagation characteristics. After studying propagation characteristics of the mode, the linear layer was replaced with a layer containing a uniaxial material. The effect of optical anisotropy of the layer on the dispersion characteristics of the nonlinear SPPs was investigated to understand the possible tunability of the mode. It has been observed that the propagation characteristics of modes supported by the waveguide can be tuned with the help of an anisotropic medium. The guiding structure could find application in the tunable components in all-optical integrated chips.