Motivated by recent advances in fabricating graphene nanostructures, we find that an electron can be trapped in Z-shaped graphene nanoconstriction with zigzag edges. The central section of the constriction operates as a single-level quantum dot, as the current flow towards the adjunct sections (rotated by 60 degree) is strongly suppressed due to mismatched valley polarization, although each section in isolation shows maximal quantum value of the conductance . We further show, that the trapping mechanism is insensitive to the details of constriction geometry, except from the case when widths of the two neighboring sections are equal. The relation with earlier studies of electron transport through symmetric and asymmetric kinks with zigzag edges is also established.