The self-screening error in electronic structure theory is the part of the self-interaction error that would remain within the GW approximation if the exact dynamically screened Coulomb interaction W were used, causing each electron to artificially screen its own presence. This introduces error into the electron density and ionization potential. We propose a simple, computationally efficient correction to GW calculations in the form of a local density functional, obtained using a series of finite training systems; in tests, this eliminates the self-screening errors in the electron density and ionization potential.