Predicting organismal phenotypes from genotype data is important for preventive and personalized medicine as well as plant and animal breeding. Although genome-wide association studies (GWAS) for complex traits have discovered a large number of trait- and disease-associated variants, phenotype prediction based on associated variants is usually in low accuracy even for a high-heritability trait because these variants can typically account for a limited fraction of total genetic variance. In comparison with GWAS, the whole-genome prediction (WGP) methods can increase prediction accuracy by making use of a huge number of variants simultaneously. Among various statistical methods for WGP, multiple-trait model and antedependence model show their respective advantages. To take advantage of both strategies within a unified framework, we proposed a novel multivariate antedependence-based method for joint prediction of multiple quantitative traits using a Bayesian algorithm via modeling a linear relationship of effect vector between each pair of adjacent markers. Through both simulation and real-data analyses, our studies demonstrated that the proposed antedependence-based multiple-trait WGP method is more accurate and robust than corresponding traditional counterparts (Bayes A and multi-trait Bayes A) under various scenarios. Our method can be readily extended to deal with missing phenotypes and resequence data with rare variants, offering a feasible way to jointly predict phenotypes for multiple complex traits in human genetic epidemiology as well as plant and livestock breeding.