Cold and drought stresses seriously affect cassava (Manihot esculenta) plant growth and yield. Recently, long noncoding RNAs (lncRNAs) have emerged as key regulators of diverse cellular processes in mammals and plants. To date, no systematic screening of lncRNAs under abiotic stress and their regulatory roles in cassava has been reported. In this study, we present the first reference catalog of 682 high-confidence lncRNAs based on analysis of strand-specific RNA-seq data from cassava shoot apices and young leaves under cold, drought stress and control conditions. Among them, 16 lncRNAs were identified as putative target mimics of cassava known miRNAs. Additionally, by comparing with small RNA-seq data, we found 42 lncNATs and sense gene pairs can generate nat-siRNAs. We identified 318 lncRNAs responsive to cold and/or drought stress, which were typically co-expressed concordantly or discordantly with their neighboring genes. Trans-regulatory network analysis suggested that many lncRNAs were associated with hormone signal transduction, secondary metabolites biosynthesis, and sucrose metabolism pathway. The study provides an opportunity for future computational and experimental studies to uncover the functions of lncRNAs in cassava.