Since the present ω meson family has not been established, in this work we carry out an investigation of the mass spectrum and Okubo-Zweig-Iizuka allowed a two-body strong decay of the S -wave and the D -wave ω mesons, and make the comparison with the experimental data of these reported ω states and the ω -like X ( 2240 ) state observed by BESIII. By this study, we not only suggest the possible assignments to these observed ω states under the framework of the ω meson family, but also predict three ω mesons ω ( 5 S ) , ω ( 2 D ) , and ω ( 4 D ) which are still missing in experiment. The present study may provide valuable information to further construct the ω meson family. Considering the present running status of BESIII, we also suggest that BESIII should pay more attention to the issue of the ω meson by accumulating more data.