Genomic imprinting is an important epigenetic factor in complex traits study, and there has recently been considerable interest in association study for quantitative traits by incorporating imprinting. However, these methods need the assumptions of Hardy-Weinberg equilibrium or only use information from families with one child. In this paper, by taking imprinting into account and making no assumption about the distribution of the quantitative traits, we propose two novel classes of Q-C-TDTI(c) and Q-C-MAX(c) family-based association tests for quantitative traits. The tests flexibly accommodate family data with missing parental genotype and with multiple siblings. Q-C-TDTI(c) is derived from a two-stage analysis, where in the first stage Q-C-PAT(c) is applied to test for imprinting effects and in the second stage we select the most appropriate statistic among three transmission disequilibrium tests for association according to the finding from Q-C-PAT(c). Another proposed Q-C-MAX(c) approach takes the maximum of the three statistics. Compared with the existing alternative methods, the simulation results demonstrate that the two proposed tests are robust to population stratification and have better performance for testing association under various scenarios. Further, the powerful and versatile Q-C-TDTI(c) test is applied to analyze Framingham Heart Study data.