Parent-of-origin effects have been pointed out to be one plausible source of the heritability that was unexplained by genome-wide association studies. Here, we consider a case-control mother-child pair design for studying parent-of-origin effects of offspring genes on neonatal/early-life disorders or pregnancy-related conditions. In contrast to the standard case-control design, the case-control mother-child pair design contains valuable parental information and therefore permits powerful assessment of parent-of-origin effects. Suppose the region under study is in Hardy-Weinberg equilibrium, inheritance is Mendelian at the diallelic locus under study, there is random mating in the source population, and the SNP under study is not related to risk for the phenotype under study because of linkage disequilibrium (LD) with other SNPs. Using a maximum likelihood method that simultaneously assesses likely parental sources and estimates effect sizes of the two offspring genotypes, we investigate the extent of power increase for testing parent-of-origin effects through the incorporation of genotype data for adjacent markers that are in LD with the test locus. Our method does not need to assume the outcome is rare because it exploits supplementary information on phenotype prevalence. Analysis with simulated SNP data indicates that incorporating genotype data for adjacent markers greatly help recover the parent-of-origin information. This recovery can sometimes substantially improve statistical power for detecting parent-of-origin effects. We demonstrate our method by examining parent-of-origin effects of the gene PPARGC1A on low birth weight using data from 636 mother-child pairs in the Jerusalem Perinatal Study.