Polygenic risk scores suffer reduced accuracy in non-European populations, exacerbating health disparities. We propose PolyPred, a method that improves cross-population polygenic risk scores by combining two predictors: a new predictor that leverages functionally informed fine-mapping to estimate causal effects (instead of tagging effects), addressing linkage disequilibrium differences, and BOLT-LMM, a published predictor. When a large training sample is available in the non-European target population, we propose PolyPred+, which further incorporates the non-European training data. We applied PolyPred to 49 diseases/traits in four UK Biobank populations using UK Biobank British training data, and observed relative improvements versus BOLT-LMM ranging from +7% in south Asians to +32% in Africans, consistent with simulations. We applied PolyPred+ to 23 diseases/traits in UK Biobank east Asians using both UK Biobank British and Biobank Japan training data, and observed improvements of +24% versus BOLT-LMM and +12% versus PolyPred. Summary statistics-based analogs of PolyPred and PolyPred+ attained similar improvements.