We study the electrical conductivity in a nodal-line semimetal with charged impurities. The screening of the Coulomb potential in this system is qualitatively different from what is found in conventional metals or semiconductors, with the screened potential phi decaying as phi alpha 1/r(2) over a wide interval of distances r. This unusual screening gives rise to a rich variety of conduction regimes as a function of temperature, doping level, and impurity concentration. In particular, nodal-line semimetals exhibit a diverging mobility alpha 1/|mu| in the limit of vanishing chemical potential mu, a linearly increasing dependence of the conductivity on temperature, sigma alpha T, and a large weak-localization correction with a strongly anisotropic dependence on magnetic field.