Drought stress has been the major constraint on peanut yield and quality, and an understanding of the function of long non-coding (lncRNAs) in the peanut drought stress response is still in its infancy. In this study, two peanut varieties with contrasting drought tolerance were used to explore the functions of lncRNAs in the peanut drought response, and the results showed that the drought-tolerant variety presented greater antioxidant enzyme activity, osmotic adjustment ability, and photosynthesis under drought conditions. There were 4329 lncRNAs identified in the two varieties, of which 535 and 663 lncRNAs were differentially expressed in NH5 and FH18, respectively. The cis targets of the differentially expressed lncRNAs were putatively involved in secondary metabolite biosynthesis and other basic metabolic processes. A total of 673 competing endogenous RNA (ceRNA) pairs were selected specifically in NH5, and the associated ceRNA network revealed six lncRNAs, MSTRG.70535.2, MSTRG.86570.2, MSTRG.86570.1, MSTRG.100618.1, MSTRG.81214.2, and MSTRG.30931.1were considered as hub nodes. They were speculated to contribute to enhancing peanut drought tolerance, such as regulating transcription and plant growth processes, thereby improving the drought stress response. In this study, lncRNAs and mRNAs interaction networks were constructed to aid a comprehensive understanding of the peanut drought stress response and form a basis for future research.