Grain weight in wheat is the product of rate and duration of grain filling (GF). GF rate represents the rate of dry matter accumulation per grain during grain fill. The lack information regarding the genetic base of GF rate prompted this study to determine kind of inheritance, genetic components and heritability for the GF rate. Nine spring wheat cultivars (Dugoklasa, Lelija, Radusa, Vesna, Bobwhite, Buckbuck, Glennson 81, Mitacore) and their F1, F2, BC1, and BC2 generations were used for investigation. In order to determine the genetic base of GF rate the additive-dominance, and six-parameter models have been used. The mean values of the F1 and F2 generations depended on the cross and were either closer to the mean of the parent with the low or higher GF rate. The additive-dominance model explained the variation of GF rate in two and six-parameter model in four crosses. Additive and dominance effects were the most responsible for GF rate in spring wheat. The most significant interaction were additive x dominance and dominance × dominance epistasis. A primary part of genetic variability for GF rate was associated with additive gene action, although dominance effects also were involved in the inheritance. Narrow-sense heritability estimates ranged from 0,35 to 0,73. Results suggested that early-generation selection for GF rate would be less effective and selection for this trait should be done in later generations.