Visual odometry (VO) is typically considered as a chicken-and-egg problem, as the localization and mapping modules are tightly-coupled. The estimation of a visual map relies on accurate localization information. Meanwhile, localization requires precise map points to provide motion constraints. This classical design principle is naturally inherited by visual-inertial odometry (VIO). Efficient localization solutions that do not require a map have not been fully investigated. To this end, we propose a novel structureless VIO, where the visual map is removed from the odometry framework. Experimental results demonstrated that, compared to the structure-based VIO baseline, our structureless VIO not only substantially improves computational efficiency but also has advantages in accuracy.