Context Functional genomics studies have highlighted genomic regions with regulatory and evolutionary significance. Such information independent of association analysis may benefit fine-mapping and genomic selection of economically important traits. However, systematic evaluation of the use of functional information in mapping, and genomic selection of cattle traits, is lacking. Also, single-nucleotide polymorphisms (SNPs) from the high-density (HD) panel are known to tag informative variants, but the performance of genomic prediction using HD SNPs together with variants supported by different functional genomics is unknown. Aims We selected six sets of functionally important variants and modelled each set together with HD SNPs in Bayesian models to map and predict protein, fat and milk yield as well as mastitis, somatic cell count and temperament of dairy cattle. Methods Two models were used, namely (1) BayesR, which includes priors of four distribution of variant effects, and (2) BayesRC, which includes additional priors of different functional classes of variants. Bayesian models were trained in three breeds of 28 000 cows of Holstein, Jersey and Australian Red and predicted into 2600 independent bulls. Key results Adding functionally important variants significantly increased the enrichment of genetic variance explained for mapped variants, suggesting improved genome-wide mapping precision. Such improvement was significantly higher when the same set of variants was modelled by BayesRC than by BayesR. Combining functional variant sets with HD SNPs improves genomic prediction accuracy in the majority of the cases and such improvement was more common and stronger for non-Holstein breeds and traits such as mastitis, somatic cell count and temperament. In contrast, adding a large number of random sequence variants to HD SNPs reduces mapping precision and has a worse or similar prediction accuracy, compared with using HD SNPs alone to map or predict. While BayesRC tended to have better genomic prediction accuracy than did BayesR, the overall difference in prediction accuracy between the two models was insignificant. Conclusions Our findings demonstrated the usefulness of functional data in genomic mapping and prediction. Implications We have highlighted the need for effective tools exploiting complex functional datasets to improve genomic prediction.