Genomic imprinting plays a pivotal role in early stage development in plants. Linkage analysis has been proven to be useful in mapping imprinted quantitative trait loci (iQTLs) underlying imprinting phenotypic traits in natural populations or experimental crosses. For correlated traits, studies have shown that multivariate genetic linkage analysis can improve QTL mapping power and precision, especially when a QTL has a pleiotropic effect on several traits. In addition, the joint analysis of multiple traits can test a number of biologically interesting hypotheses, such as pleiotropic effects vs close linkage. Motivated by a triploid maize endosperm dataset, we extended the variance components linkage analysis model incorporating imprinting effect proposed by Li and Cui (2010) to a bivariate trait modeling framework, aimed to improve the mapping precision and to identify pleiotropic imprinting effects. We proposed to partition the genetic variance of a QTL into sex-specific allelic variance components, to model and test the imprinting effect of an iQTL on two traits. Both simulation studies and real data analysis show the power and utility of the method.