The paper presents a study on the influence of ground waste glass cullet, introduced as a component of Portland cements in the amounts of 5% and 35% by mass, on the properties of pastes and mortars. The pozzolanic nature of the additive was confirmed – the long-term compressive strength of cement composites has increased, compared to the reference sample. However, a decrease in the early compressive strength was observed. Replacing part of the Portland clinker with ground waste glass cullet resulted in the reduction of the heat of hydration. It was determined that the degree of grinding has a significant impact on the activity of waste glass cullet – in the case of the cullet ground to 5000 cm²/g, the beginning of the pozzolanic reaction was observed after 7 days, whereas for the cullet ground to 3000 cm²/g, the reaction was severely delayed. In the course of one year, no negative impact of the alkali-silica reaction on the strength and microstructure of mortars and pastes was observed, however, a longer study needs to be conducted to verify the results. The research proves that waste glass cullet can be potentially used as a main component of Portland cements, with no adverse effects on the properties of the composites.