We estimated the heritability of growth-related traits (weight and length at ages one summer, first spring and two summers) in a synthetic mirror carp strain (HSM) in the Czech Republic. The four generation pedigree was obtained from parentage assignment of three factorial mating designs with microsatellite markers, and included 195 fish without phenotypes (48 G0, 147 G1) and 1321 fish with phenotypes (674 G2, 647 G3). Animal model heritability estimates over generations were in the range 0.21–0.33 for length and in the range 0.31–0.44 for weight. The genetic correlation between length and weight was high (0.97). The correlations between growth measurements in the first and in the second summer of age were moderate to low (0.34–0.67). Divergent selection for length at two summers of age was performed on G2 fish, and response to selection was evaluated by comparing the offspring of the selected sires in G3, in a communal test where genetic groups were identified by microsatellite parentage assignment. The response to upwards selection was moderate and indicated a realized heritability value of 0.24 to 0.34. No response to downwards selection was observed. We conclude that although selection for growth seems to be feasible in common carp, it would be a long-term process before results are visible.