Polygenic risk scores (PRS) use the results of genome-wide association studies (GWAS) to predict quantitative phenotypes or disease risk at an individual level, and provide a potential route to the use of genetic data in personalized medical care. However, a major barrier to the use of PRS is that the majority of GWAS come from cohorts of European ancestry. The predictive power of PRS constructed from these studies is substantially lower in non-European ancestry cohorts, although the reasons for this are unclear. To address this question, we investigate the performance of PRS for height in cohorts with admixed African and European ancestry, allowing us to evaluate ancestry-related differences in PRS predictive accuracy while controlling for environment and cohort differences. We first show that the predictive accuracy of height PRS increases linearly with European ancestry and is partially explained by European ancestry segments of the admixed genomes. We show that recombination rate, differences in allele frequencies, and differences in marginal effect sizes across ancestries all contribute to the decrease in predictive power, but none of these effects explain the decrease on its own. Finally, we demonstrate that prediction for admixed individuals can be improved by using a linear combination of PRS that includes ancestry-specific effect sizes, although this approach is at present limited by the small size of non-European ancestry discovery cohorts.