A linear cycle in a 3-uniform hypergraph H is a cyclic sequence of hyperedges such that any two consecutive hyperedges intersect in exactly one element and non-consecutive hyperedges are disjoint. Let α(H) denote the size of a largest independent set of H. We show that the vertex set of every 3-uniform hypergraph H can be covered by at most α(H) edge-disjoint linear cycles (where we accept a vertex and a hyperedge as a linear cycle), proving a weaker version of a conjecture of Gyárfás and Sárközy. © The authors