Aerogels have been considered as an ideal material for thermal insulation. Unfortunately, their application in textiles is greatly limited by their fragility and poor processability. We overcame these issues by encapsulating the aerogel fiber with a stretchable layer, mimicking the core-shell structure of polar bear hair. Despite its high internal porosity over 90%, our fiber is stretchable up to 1000% strain, which is greatly improved compared with that of traditional aerogel fibers (~2% strain). In addition to its washability and dyeability, our fiber is mechanically robust, retaining its stable thermal insulation property after 10,000 stretching cycles (100% strain). A sweater knitted with our fiber was only one-fifth as thick as down, with similar performance. Our strategy for this fiber provides rich possibilities for developing multifunctional aerogel fibers and textiles.