To increase the predictive accuracy of genomic selection, large-scale phenotypic and genomic data is needed, which results in enormous consumption of computational resources, hampering the feasibility of genomic selection in return. In order to address computational limitation, a rapid genomic selection method HEAPY|A is developed in this study, combining Haseman-Elston (HE) model and algorithm for proven and young (APY). The proposed approach utilizes (i) HE regression to estimate the heritability and then (ii) APY to solve the inverse of the large matrix in best linear prediction (BLP); both HE and APY can reduce the computational cost compared with conventional techniques. When the size of a core population is half of that of a large training population, GBLUP|A, HEAPY|A, and HEBLP|A have similar performance in simulation studies (the core population can be further reduced if the training population size is further increased). When the size of a core population is half of that of a small training population, the predictive accuracy of HEAPY|A is a little lower than that of GBLUP|A and HEBLP|A in simulation study and empirical data—an Arabidopsis thaliana F2 population. HEAPY|A helps in predicting large genomic selection dataset with comparable accuracy without significant expense of time seen in traditional genomic selection algorithm.