A Z-shaped junction constructed by a few-nanometer-long armchair-edged boron nitride nanoribbon (ABNNR) sandwiched between two semi-infinite zigzag-edged BNNR electrodes with different hydrogen-passivated edge treatment is proposed, and its spin-dependent electronic transport is studied by ab initio calculations. It is found that a short ABNNR exhibits metallic behavior and can be used as a conduction channel. Interestingly, the spin-filtering and rectification effects exist in the junctions without any edge passivation or with boron-edge passivation. The analysis on the projected density of states and spatial distribution of molecular projected self-consistent Hamiltonian eigenstates gives an insight into the observed results for the system. Our results suggest that a BNNR-based nanodevices with spin-filtering and rectification effects may be synthesized from an hexagonal boron nitride sheet by properly tailoring and edge passivation.