The use of fly ash in cement composites adversely affects its mechanical properties during the first days of mixture curing. Modern technology, in the form of an admixture containing the hydrated calcium silicates, allows to accelerate the hardening and binding process of concrete. In this paper, studies on the influence of the admixture on properties of concretes with the ordinary Portland cements (OPC) containing the addition of siliceous fly ash (FA) have been carried out. As part of the experimental research, the authors conducted a series of studies for cement pastes modified with the addition of FA and the CSH nano-admixture (NA). In order to compare the mixtures, the following tests of cement pastes were carried out: the compressive and flexural strength, heat of hydration, SEM and rheological shrinkage. The mechanical parameters were tested after 4, 8, 12 and 24 h. The hydration heat test and microstructure analysis were carried out during the first 24 h of the concrete curing. All tests were carried out on the standard samples. On the basis of the heat of hydration test, much higher hydration heat was found in mixtures modified with the NA. During the shrinkage test, a positive effect of the NA was observed—the shrinkage during the first 28 days of mixture curing was lower than in the reference samples. The application of the CSH nano-admixture to cement pastes with the addition of FA has brought positive effects. Apart from a significant increase in strength in the first 24 h of mixture curing, a reduction in the rheological shrinkage was observed. The admixture can be successfully used in the ash concretes, in which a higher early strength is required.