We present optical and near-IR photometry and spectroscopy of SN 2013L for the first 4 yr post-explosion. SN 2013L was a moderately luminous (M-r = -19.0) Type IIn supernova (SN) that showed signs of strong shock interaction with the circumstellar medium (CSM). The CSM interaction was equal to or stronger to SN 1988Z for the first 200 d and is observed at all epochs after explosion. Optical spectra revealed multicomponent hydrogen lines appearing by day 33 and persisting and slowly evolving over the next few years. By day 1509, the Ha emission was still strong and exhibiting multiple peaks, hinting that the CSM was in a disc or torus around the SN. SN 2013L is part of a growing subset of SNe IIn that shows both strong CSM interaction signat...