The rapid progress and plummeting costs of human-genome sequencing enable the availability of large amount of personal biomedical information, leading to one of the most important concerns — genomic data privacy. Since personal biomedical data are highly correlated with relatives, with the increasing availability of genomes and personal traits online (i.e., leakage unwittingly, or after their releasing intentionally to genetic service platforms), kin-genomic data privacy is threatened. We propose new inference attacks to predict unknown Single Nucleotide Polymorphisms (SNPs) and human traits of individuals in a familial genomic dataset based on probabilistic graphical models and belief propagation. With this method, the adversary can predict the unobserved genomes or traits of targeted individuals in a family genomic dataset where some individuals’ genomes and traits are observed, relying on SNP-trait association from Genome-Wide Association Study (GWAS), Mendel’s Laws, and statistical relations between SNPs. Existing genome inferences have relatively high computational complexity with the input of tens of millions of SNPs and human traits. Then, we propose an approach to publish genomic data with differential privacy guarantee. After finding an approximate distribution of the input genomic dataset relying on Bayesian networks, a noisy distribution is obtained after injecting noise into the approximate distribution. Finally, synthetic genomic dataset is sampled and it is proved that any query on synthetic dataset satisfies differential privacy guarantee.