Background: Breastfeeding promotes healthy growth in very-preterm-born infants (VPI), but extra nutritional supply is needed to ensure catch-up growth and brain development. Objectives: To investigate how different types of post-discharge nutrition affect growth until 6 years of age in children born VPI. Methods: This was a 6-year follow-up study of 281 VPI. Median gestational age (GA) was 30 + 0 weeks (range 24–32 weeks). When breastfed at discharge, they were randomized to unfortified human milk (UHM) or fortified human milk (FHM). If not breastfed at discharge, they received a preterm formula (PF). The intervention lasted until 4 months of corrected age (CA). At 6 years CA, their height and weight were measured. Results: A total of 239 children participated in the follow-up. UHM-feeding compared to both PF- and FHM-feeding resulted in a slower but continuous catch-up growth until 6 years of age. Participants born small-for-GA compared to appropriate-for-GA more often demonstrated continuous catch-up growth until 6 years of age (p = 0.018). Rapid weight growth (a change in z score > 1 SD during a short time period) was found to be most pronounced from 34 weeks post-menstrual age to 2 months CA, and especially among those fed PF (p = 0.002 vs. UHM, p = 0.07 vs. FHM). Conclusions: Catch-up growth occurred mainly before discharge, regardless of the feeding group. UHM-fed infants demonstrated catch-up growth that was slower, but extended until 6 years of age. Rapid weight growth was most pronounced shortly after discharge and especially if PF-fed.