People in the Solomon Islands today are considered to have derived from Asian- and Papuan-related ancestors. Papuan-related ancestors colonized Near Oceania about 47,000 years ago, and Asian-related ancestors were Austronesian (AN)-speaking population, called Lapita, who migrated from Southeast Asia about 3,500 years ago. These two ancestral populations admixed in Near Oceania before the expansion of Lapita people into Remote Oceania. To understand the impact of the admixture on the adaptation of AN-speaking Melanesians in Near Oceania, we performed the genome-wide single nucleotide polymorphism (SNP) analysis of 21 individuals from Munda, the main town of the New Georgia Islands in the western Solomon Islands. Population samples from Munda were genetically similar to other Solomon Island population samples. The analysis of genetic contribution from the two different ancestries to the Munda genome revealed significantly higher proportions of Asian- and Papuan-related ancestries in the region containing the annexin A1 (ANXA1) gene (Asian component > 82.6%) and in the human leukocyte antigen (HLA) class II region (Papuan component > 85.4%), respectively. These regions were suspected to have undergone natural selection since the time of admixture. Our results suggest that admixture had affected adaptation of AN-speaking Melanesians in the Solomon Islands.