We study the quasi-bound state and the transport properties in the T-shaped graphene nanoribbon consisting of a metallic armchair-edge ribbon connecting to a zigzag-edge sidearm. We systematically study the condition under which there are quasi-bound states in the system for a wide range of the system size. It is found that when the width of the sidearm is about half of the width of the armchair leads, there is a quasi-bound state trapped at the intersection of the T-shape structure. The quasi-bound states are truly localized in the sidearm but have small continuum components in the armchair leads. The quasi-bound states have strong effect on the transport between the armchair leads through the Fano effect, but do not affect the transport between the armchair lead and the sidearm.
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