Context. Long gamma-ray bursts (GRBs) can potentially be used as a tool to study star formation and recent gas accretion onto galaxies. However, the information about gas properties of GRB hosts is scarce. In particular, very few carbon monoxide (CO) line detections of individual GRB hosts have been reported. It has also been suggested that GRB hosts have lower molecular gas masses than expected from their star formation rates (SFRs). Aims. The objectives of this paper are to analyse molecular gas properties of the first substantial sample of GRB hosts and test whether they are deficient in molecular gas. Methods. We obtained CO(2-1) observations of seven GRB hosts with the APEX and IRAM 30 m telescopes. We analysed these data toget...