Exchange coupling at the interface of an antiferromagnet and a ferromagnet is the major route toward the future magnetoelectric applications of multiferroic bismuth ferrite at room temperature. By using angle-resolved longitudinal magneto-optic Kerr effect microscopy, we have investigated the exchange anisotropy in a ferromagnetic Co layer adjacent to electrically aligned straight-stripe mixed-phase-boundary (MPB) regions of La-5%-doped BiFeO3. We have found that the magnetic easy axis of the exchange-coupled Co layer becomes parallel to the in-plane crystallographic axis nearest to the adjacent MPB elongation axis. The coercive field of the exchange-coupled Co layer along the magnetic easy axis has prominently increased by similar to 66 Oe, i.e., 30 times larger than that of a control sample (2.3 Oe), wherein a 5-nm-thick nonmagnetic Ta spacer is placed between the antiferromagnetic and ferromagnetic layers and thus it is intended to have only the shape anisotropy arising from the surface nanostructure of the MPB regions. The finding opens a promising avenue for magnetoelectric applications at room temperature.