Cultural Transmission of Reproductive Success (CTRS) has been observed in many human populations as well as other animals. It consists in a positive correlation of non-genetic origin between the progeny size of parents and children. This correlation can result from various factors, such as the social influence of parents on their children, the increase of children’s survival through allocare from uncle and aunts, or the transmission of resources. Here, we study the evolution of genomic diversity through time under CTRS. We show that CTRS has a double impact on population genetics: (1) effective population size decreases when CTRS starts, mimicking a population contraction, and increases back to its original value when CTRS stops; (2) coalescent trees topologies are distorted under CTRS, with higher imbalance and higher number of polytomies. Under long-lasting CTRS, effective population size stabilises but the distortion of tree topology remains, which yields U-shaped Site Frequency Spectra (SFS) under constant population size. We show that this CTRS’ impact yields a bias in SFS-based demographic inference. Considering that CTRS was detected in numerous human and animal populations worldwide, one should be cautious that inferring population past histories from genomic data can be biased by this cultural process.