The present report deals with the development of a cost-effective, solution-processable and nanoparticulated In2O3 thin-film memristive device for application in multilevel resistive random access memory (RRAM). The structural, morphological, elemental and electrical characterizations are carried out with the help of x-ray diffractometry, scanning electron microscopy, photoluminescence spectroscopy, Fourier transform infrared spectroscopy, x-ray photoelectron spectroscopy and a memristor characterization system. The electrical characterizations reveal that the nanoparticulated In2O3 thin-film memristive device is free from the electroforming process and shows self-rectifying and self-compliance memory effects. Furthermore, we have demonstrated multilevel resistive switching with excellent memory properties of endurance (10 000 switching cycles) and retention (2 ks). Interestingly, the device shows a good memory window (10 for all cases), and multilevel resistance states are not degraded during endurance and retention memory tests. The uniformity and stability in multilevel resistive switching are further confirmed by statistical calculations. Furthermore, the nanoparticulated In2O3 thin-film memristive device mimics the property of paired-pulse facilitation of a biological synapse. A detailed analysis of electrical results suggests that the Schottky effect is responsible for the device conduction. In a nutshell, the nanoparticulated In2O3 memristive device is suitable for future multilevel RRAM application and is a promising candidate for development of an electronic synaptic device for application in neuromorphic computing.