In this study, edge-oxidized graphene oxide (EOGO) was used as an additive in fly ash (FA) geopolymer paste. The effect of EOGO on the properties of the fly ash geopolymer was investigated. EOGO was added to the FA geopolymer at four different percentages (0%, 0.1%, 0.5% and 1%), and the mixture was cured under two different conditions: room curing (~20 °C) and heat curing (~60 °C). To characterize the FA-EOGO geopolymer, multiple laboratory tests were employed, including compressive strength, Free-Free Resonance Column (FFRC), density, water absorption, and setting tests. The FFRC test was used to evaluate the stiffness at small strain (Young's modulus) via the resonance of the specimen. The mechanical test results showed that the strength and elastic modulus were high during heat curing, and the highest compressive strength and elastic modulus were achieved at 0.1% EOGO. In the physical test, 0.1% EOGO had the highest density and the lowest porosity and water absorption. As a result of the setting time test, as the EOGO content increased, the setting time was shortened. It is concluded that the optimum proportion of EOGO is 0.1% in FA geopolymer paste.