Remote Attestation (RA) is a security service by which a Verifier (Vrf) can verify the platform state of a remote Prover (Prv). However, in most existing RA schemes, the Prv might be vulnerable to denial of service (DoS) attacks due to the interactive challenge-response methodology while there is no authentication about the challenge. Worse, many schemes cannot effectively detect mobile malware that can be inactive during the on-demand attestation launched by the Vrf. In this paper, we propose a self-measurement RA for SGX-based platforms, which can effectively mitigate DoS attacks and defend against mobile malware. To this end, a two-way identity authentication is first enforced between the Prv and Vrf with the help of a blockchain system, in which a shared session key is also generated. Secondly, trigger conditions of measurements on the Prv’s side are time points generated by the Prv self instead of Vrf’s requests. The Vrf can retrieve multiple selfmeasurement results during one execution of the protocol to monitor the Prv’s platform over a period of time continuously, which can detect mobile malware effectively. Our scheme utilizes SGX to provide the runtime protection for sensitive information such as session key, self-measurement code, time points of self-measurements, and self-measurement results, making a higher security guarantee. In addition, the session key, time points of self-measurements, and self-measurement code can be changed or upgraded, making our scheme more flexible and scalable. The simulation implementation and results show that our scheme is feasible and practical.