Adaptor signature, also known as scriptless script, is an important cryptographic technique that can be used to solve the problems of poor scalability and low transaction throughput in blockchain applications such as cryptocurrency. An adaptor signature can be seen as an extension of a digital signature on hard relations, and it ties together the authorization with witness extraction and has many advantages in blockchain applications, such as (1) low on-chain cost; (2) improved fungibility of transactions; (3) advanced functionality beyond the limitation of the blockchain’s scripting language. SM2 signature is the Chinese national standard signature algorithm and has been widely used in various important information systems. This work designs an efficient SM2-based adaptor signature with batch proofs and gives security proofs under the random oracle model. The scheme avoids to generate zero-knowledge proofs used in the pre-signing phase based on the structure of SM2 signature and is more efficient than existing ECDSA/SM2-based adaptor signature. Specifically, the efficiency of pre-signature generation is increased by 4 times, and the efficiency of pre-signature verification is increased by 3 times. Then, based on distributed SM2 signature, this work develops distributed SM2-based adaptor signature which can avoid the single point of failure and improve the security of signing key. Finally, in real-world applications, this work gives a secure and efficient batch atomic swap protocol for one-to-many scenarios based on SM2-based adaptor signature.