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By employing nonequilibrium Green’s function methods in combination with density functional theory, we investigate electronic structures and transport properties of the armchair graphene nanoribbon (AGNR) heterojunctions consisting of the sulfur(S)-doped AGNR and the pristine one, which are realizable in experiments. The results show that such heterojunctions own inherent rectifying behaviour with a high rectifying ratio up to 10 4 , and the rectifying direction is totally controllable by choosing the width of ribbon. It is revealed that the rectifying mechanism is driven by easily pinning valence-band maximum (VBM) on the conduction band minimum (CBM) under forward biases but hardly pinning under reverse biases, and the rectifying direction is described by the interrelationship of the band gap between the S-doped AGNR and AGNR segments. Our findings provide a route for the design of AGNR-based rectifiers with controllable direction in molectronics.