Anisotropic magnetic properties of a layered kagome-like system Cu ₃Bi(SeO ₃) ₂O ₂Br have been studied by bulk magnetization and magnetic susceptibility measurements as well as powder and single-crystal neutron diffraction. At T _N=27.4 K the system develops an alternating antiferromagnetic order of (ab) layers, which individually exhibit canted ferrimagnetic moment arrangement, resulting from the competing ferro- and antiferro-magnetic intralayer exchange interactions. A magnetic field B _C∼0.8 T applied along the c axis (perpendicular to the layers) triggers a metamagnetic transition, when every second layer flips, i.e., resulting in a ferrimagnetic structure. Significantly higher fields are required to rotate the ferromagnetic component towards the b axis (∼7T) or towards the a axis (∼15T). The estimates of the exchange coupling constants and features indicative of an XY character of this quasi-2D system are presented.