Organo-metal halide perovskite field-effect transistors present serious challenges in terms of device stability and hysteresis in the current-voltage characteristics. Migration of ions located at grain boundaries and surface defects in the perovskite film are the main reasons for instability and hysteresis issues. Here, we introduce a perovskite grain molecular cross-linking approach combined with amine-based surface passivation to address these issues. Molecular cross-linking was achieved through hydrogen bond interactions between perovskite halogens and dangling bonds present at grain boundaries and a hydrophobic cross-linker, namely diethyl-(12-phosphonododecyl)phosphonate, added to the precursor solution. With our approach, we obtained smooth and compact perovskite layers composed of tightly bound grains hence significantly suppressing the generation and migration of ions. Moreover, we achieved efficient surface passivation of the perovskite films upon surface treatment with an amine-bearing polymer, namely polyethylenimine ethoxylated. With our synergistic grain and surface passivation approach, we were able to demonstrate the first perovskite transistor with a complete lack of hysteresis and unprecedented stability upon continuous operation under ambient conditions. Added to the merits are its ambipolar transport of opposite carriers with balanced hole and electron mobilities of 4.02 and 3.35 cm2 V-1 s-1, respectively, its high Ion/Ioff ratio >104 and the lowest sub-threshold swing of 267 mV dec-1 reported to date for any perovskite transistor. These remarkable achievements obtained through a cost-effective molecular cross-linking of grains combined with amine-based surface passivation of the perovskite films open a new era and pave the way for the practical application of perovskite transistors in low-cost electronic circuits.