Allogeneic umbilical cord blood (UCB) donation is a pro-social behaviour directed to strangers that has a certain cost for the donor. Although the promotion of such behaviour is an important goal for many countries' health systems, little is known about the reasons that would lead to it. With this study, we explored how the impact of social closeness on altruism and trust could be related to UCB donation in a sample of new-mothers (N = 167). Participants played hypothetical Dictator and Trust games with socially close (e.g., parents) or distant (e.g., strangers) others. They donated more money to parents and siblings compared to cousins, friends and strangers and they trusted more parents, siblings and friends than cousins and strangers. Interestingly, the lower the impact of social closeness on altruism (i.e., generosity towards socially distant others), the higher the intention and the actual probability of UCB donation. A mediation analysis has shown that the relationship between social closeness on altruism and UCB donation was mediated by objective intention to donate (i.e., having followed all the procedures needed). These findings show that other-oriented motivations towards distant others might have important practical implications in identifying the targets of interventions for the promotion of UCB donation.