The far-red-impaired response 1 (FAR1) transcription family were initially identified as important factors for phytochrome A (phyA)-mediated far-red light signaling in Arabidopsis; they play crucial roles in controlling the growth and development of plants. The reported reference genome sequences of Arachis, including A. duranensis, A. ipaensis, A. monticola, and A. hypogaea, and its related species Glycine max provide an opportunity to systematically perform a genome-wide identification of FAR1 homologous genes and investigate expression patterns of these members in peanut species. Here, a total of 650 FAR1 genes were identified from four Aarchis and its closely related species G. max. Of the studied species, A. hypogaea contained the most (246) AhFAR1 genes, which can be classified into three subgroups based on phylogenic relationships. The synonymous (Ks) and non-synonymous (Ka) substitution rates, phylogenetic relationship and synteny analysis of the FAR1 family provided deep insight into polyploidization, evolution and domestication of peanut AhFAR1 genes. The transcriptome data showed that the AhFAR1 genes exhibited distinct tissue- and stage-specific expression patterns in peanut. Three candidate genes including Ahy_A10g049543, Ahy_A06g026579, and Ahy_A10g048401, specifically expressed in peg and pod, might participate in pod development in the peanut. The quantitative real-time PCR (qRT-PCR) analyses confirmed that the three selected genes were highly and specifically expressed in the peg and pod. This study systematically analyzed gene structure, evolutionary characteristics and expression patterns of FAR1 gene family, which will provide a foundation for the study of genetic and biological function in the future.