Germanium selenide (GeSe) nanoribbons as quasi-one-dimensional materials have been expected to host tunable fascinating electronic properties due to the edge state and quantum confinement effect. Herein, the effect on the electronic structures and transport properties of the zigzag GeSe nanoribbons (ZGeSeNR) of different functional groups passivation are systematically studied using a combination of density functional theory and non-equilibrium Grimm function. The N-, P-, and S-passivated ZGeSeNRs are metallic, while F-, Cl-, OH-, and H-passivated ones exhibit semiconductor properties. The rectification behavior is found in the lateral ZGeSeNR heterojunctions composed of metal-semiconductor contact, and the rectification performance can be modulated by changing the edge passivation group, the ribbon width, and the length of the scattering region. Especially, the highest rectification ratio (RR) reaches 9.2Ⅹ106 in the H-ZGeSeNR-S heterojunctions, in which the left and right half-edge atoms are passivated by H- and S- groups respectively. These results are useful for the design of nanoscale rectifiers based on ZGeSeNRs.