Attribute-based signature (ABS) schemes play a vital role to accomplish authentication and signer privacy simultaneously. In recent years, cryptographic primitives are deployed on insecure devices such as mobile devices; thereby, secret key exposure seems inevitable. To alleviate the impact of key exposure in ABS scenarios, the authors apply the method of key insulation to ABS and construct the first signature-policy attribute-based key-insulated signature (ABKIS) scheme. The proposed construction supports expressive monotone Boolean functions as signing predicates and preserves signer privacy. Their ABKIS scheme is key-insulated and strong key-insulated secure under computational Diffie-Hellman exponent assumption. To the best of their knowledge, the proposed ABKIS is the first ABS scheme in signature-policy flavour dealing with key exposure problems employing key-insulation mechanism.