Abstract Ten protostellar outflows in the Orion molecular clouds were mapped in the 12 CO/ 13 CO J = 6 → 5 and 12 CO J = 7 → 6 lines. The maps of these mid- J CO lines have an angular resolution of about 10″ and a typical field size of about 100″. The physical parameters of the molecular outflows were derived, including mass transfer rates, kinetic luminosities, and outflow forces. The outflow sample was expanded by reanalyzing archival data of nearby low-luminosity protostars to cover a wide range of bolometric luminosities. Outflow parameters derived from other transitions of CO were compared. The mid- J ( J up ≈ 6) and low- J ( J up ≤ 3) CO line wings trace essentially the same outflow component. By contrast, the high- J (up to J up ≈ 50) line-emission luminosity of CO shows little correlation with the kinetic luminosity from the J = 6 → 5 line, which suggests that they trace distinct components. The low-/mid- J CO line wings trace long-term outflow behaviors, while the high- J CO lines are sensitive to short-term activities. The correlations between the outflow parameters and protostellar properties are presented, which shows that the strengths of molecular outflows increase with bolometric luminosity and envelope mass.