Hi-COLA runs fast approximate N-body simulations of non-linear structure formation in reduced Horndeski gravity (Horndeski theories with luminal gravitational waves). It is generic with respect to the reduced Horndeski class. Given an input Lagrangian, Hi-COLA's front-end dynamically constructs the appropriate field equations and consistently solves for the cosmological background, linear growth, and screened fifth force of that theory. This is passed to the back-end, which runs a hybrid N-body simulation at significantly reduced computational and temporal cost compared to traditional N-body codes. By analyzing the particle snapshots, one can study the formation of structure through statistics such as the matter power spectrum.