We show that surface plasmon polaritons (SPPs) can be concentrated to subwavelength dimensions in a nanoscale dielectric wedge on a metal substrate. An adiabatic model explains how SPPs propagating on a Ag substrate covered with a thin Si film of slowly increasing thickness become highly confined inside the Si layer. Simulations predict strong subwavelength focusing near the surface plasmon resonance frequency. Unlike alternative strategies, this method does not require the nanoscale shaping of metal surfaces.