A paired-dominating set of a graph G is a dominating set of vertices whose induced subgraph has a perfect matching. The paired-domination number γpr(G) is the minimum cardinality of a paired-dominating set of G. In this paper, we prove the conjecture of Goddard and Henning (2009) stating that if G is a connected cubic graph of order n and G is different from the Petersen graph, then γpr(G)≤4n/7.