Close to the Fermi energy, nodal loop semimetals have a torus-shaped, strongly anisotropic Fermi surface which affects their transport properties. Here we investigate the non-equilibrium dynamics of nodal loop semimetals by going beyond linear response and determine the time evolution of the current after switching on a homogeneous electric field. The current grows monotonically with time for electric fields perpendicular to the nodal loop plane, however, it exhibits non-monotonical behavior for field orientations aligned within the plane. After an initial non-universal growth ~Et, the current first reaches a plateau ~E. Then, for perpendicular directions, it increases while for in-plane directions it decreases with time to another plateau, still ~E. These features arise from interband processes. For long times or strong electric fields, the current grows as ~E^(3/2)t or ~E^3t^2 for perpendicular or parallel electric fields, respectively. This non-linear response represents an intraband effect where the large number of excited quasiparticles responds to the electric field. Our analytical results are benchmarked by the numerical evaluation of the current from continuum and tight-binding models of nodal loop semimetals.