We studied the diffusion of charged gold nanoparticles within a semidilute solution of weakly charged polyelectrolyte, polyacrylic acid (PAA) of high molecular weight (Mw = 106 g mol-1) by using fluorescence correlation spectroscopy (FCS). Nanoparticle size (d) was varied between 5 nm to 40 nm and PAA volume fraction (φ) in water ranged from about 8φ* to 33φ*, where φ* is the overlap volume fraction. The reduced diffusion coefficient - defined as -D/Do, where D is the diffusion coefficient in PAA solution and Do is that in neat water - has a weak dependence on the particle size. D follows a power law of the form ∼φ-0.5, which can be explained by a mean-field hydrodynamic theory in porous medium. Additional, rheology measurements showed a zero shear rate viscosity and shear thinning, which are typical of high molecular weight polyelectrolytes.