Genomic imprinting is a genetic phenomenon in which certain alleles are differentially expressed in a parent-of-origin-specific manner, and plays an important role in the study of complex traits. For a diallelic marker locus in human, the parental-asymmetry tests Q-PAT(𝑐) with any constant 𝑐 were developed to detect parent-of-origin effects for quantitative traits. However, these methods can only be applied to deal with nuclear families and thus are not suitable for extended pedigrees. In this study, by making no assumption about the distribution of the quantitative trait, we first propose the pedigree parental-asymmetry tests Q-PPAT(𝑐) with any constant 𝑐 for quantitative traits to test for parent-of-origin effects based on nuclear families with complete information from general pedigree data, in the presence of association between marker alleles under study and quantitative traits. When there are any genotypes missing in pedigrees, we utilize Monte Carlo (MC) sampling and estimation and develop the Q-MCPPAT(𝑐) statistics to test for parent-of-origin effects. Various simulation studies are conducted to assess the performance of the proposed methods, for different sample sizes, genotype missing rates, degrees of imprinting effects and population models. Simulation results show that the proposed methods control the size well under the null hypothesis of no parent-of-origin effects and Q-PPAT(𝑐) are robust to population stratification. In addition, the power comparison demonstrates that Q-PPAT(𝑐) and Q-MCPPAT(𝑐) for pedigree data are much more powerful than Q-PAT(𝑐) only using two-generation nuclear families selected from extended pedigrees.