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This paper analyzes various high-κ dielectrics for low leakage AlGaN (Aluminium Gallium Nitride)/GaN (Gallium Nitride) MIS-HEMT (Metal Insulator Semiconductor—High Electron Mobility Transistor) device. The investigation is carried out by examining different attributes such as the dielectric constant, conduction band offset, and energy band gap of the dielectric which are crucial for a good dielectric-AlGaN interface. This work also computes the values of band offsets of different dielectrics to AlGaN analytically. The selection of the most promising dielectric is done using three different multi-criteria decision making methods (MCDM) namely the Ashby, VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje in Serbian, meaning Multicriteria Optimization and Compromise Solution) and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). All the analyses point to La2O3 as the best gate dielectric for AlGaN/GaN MIS-HEMT device.