We have developed an ac inductive technique that measures local critical current densities J_c of large bulk and thick-film superconductors. In this method an ac magnetic field is generated by an ac drive current (I₀cosωt) in a small flat coil placed just above the superconductor, and a third-harmonic voltage (V₃cos3ωt) generated in the same coil due to the nonlinear magnetic response of type-II superconductors is measured. Because this V₃ (due to the first mechanism by flux penetration) is proportional to I₀² and inversely proportional to J_c, J_c can be measured in the surface region (typically down to Λ₀ ~ 0.1 mm beneath the surface) of the superconductor by measuring V₃ as a function of I₀. In case of the thick-film superconductor, it is also possible to measure the J_c for the total thickness. The I₀ vs V₃ curves suddenly change the curvature at a threshold current I_th when the magnetic field penetrates the bottom surface of the film (the second mechanism). Because I_th is proportional to the product of J_c and the film thickness d, we can obtain the average J_c for the total thickness from I_th.