Homeostasis is essential in biological neural networks, optimizing information processing and experience-dependent learning by maintaining the balance of neuronal activity. However, conventional two-terminal memristors have limitations in implementing homeostatic functions due to the absence of global regulation ability. Here, three-terminal oxide memtransistor-based homeostatic synapses are demonstrated to perform highly linear synaptic weight update and enhanced accuracy in neuromorphic computing. Particularly, by leveraging the gate control of contact-engineered indium-gallium-zinc-oxide (IGZO) memtransistor, synaptic weight scaling is enabled for high-linearity and precision neuromorphic computing. Moreover, sinusoidal control of gate voltage is demonstrated, possibly enabling the emulation of higher-order synaptic functions. The device structure of IGZO memtransistor is optimized regarding the source/drain electrode materials and an interfacial layer inserted between the IGZO channel and source electrode. As a result, memtransistors exhibiting high current switching ratio of >10⁴ and reliable endurance characteristics are obtained. Furthermore, through the adaptation of synaptic scaling, emulating the homeostasis, non-linearity values of 0.01 and -0.01 are achieved for potentiation and depression, respectively, exhibiting a recognition accuracy of 91.77% for digit images. It is envisioned that the contact-engineered IGZO memtransistors hold significant promise for implementing the homeostasis in neuromorphic computing for high linearity and high efficiency.