Insect general odorant-binding proteins (GOBPs) play irreplaceable roles in filtering, binding, and transporting host odorants to olfactory receptors. Grapholita funebrana (Treitscheke) (Lepidoptera: Tortricidae), an economically important pest of fruit crops, uses fruit volatiles as cues to locate host plants. However, the functions of GOBPs in G. funebrana are still unknown. Three GOBP genes, namely, GfunGOBP1, GfunGOBP2, and GfunGOBP3, were cloned, and their expression profiles in different tissues were detected by the method of real-time quantitative PCR (RT-qPCR). The binding properties of recombinant GfunGOBPs (rGfunGOBPs) to various ligands were investigated via fluorescence binding assays. The three GfunGOBPs were mainly expressed in the antennae of both male and female moths. All these three rGfunGOBPs could bind to sex pheromones, while having varying affinities toward these pheromones. The three rGfunGOBPs also displayed a wide range of ligand-binding spectrums with tested host odorants. The rGfunGOBP1, rGfunGOBP2, and rGfunGOBP3 bound to 34, 33, and 30 out of the 41 tested odorants, respectively. Three rGfunGOBPs had overlapping binding activities to β-myrcene, (-)-α-phellandrene, and ethyl isovalerate with the Ki less than 3.0 µM. The rGfunGOBP1 and rGfunGOBP3 could selectively bind to several insecticides, whereas rGfunGOBP2 could not. Three rGfunGOBPs had the dual functions of selectively binding to sex pheromones and host odorants. Moreover, the rGfunGOBP1 and rGfunGOBP3 can also serve as ‘signal proteins’ and bind to different insecticides. This study contributed to elucidating the potential molecular mechanism of the olfaction for G. funebrana, and thereby promotes the development of effective botanical attractants or pheromone synergists to control G. funebrana.