In healthcare wireless sensor networks (HWSNs), a patient's body usually contains several wearable or implantable wireless sensors which generate and transmit physiological data to a medical server (MS) where authorised medical professionals can access relevant medical data for efficient patient's diagnosis and treatments. To achieve data integrity and authenticity, aggregate signature is generally used. Several certificateless aggregate signature (CL-AS) schemes have been proposed to address the problems in the traditional public key cryptography. However, the performances of the existing CL-AS schemes are sometimes unsatisfactory. In this work, we propose a novel pairing-free certificateless aggregate signature scheme with strong anonymity for HWSN. We show that the scheme is provably secure against Type I and Type II adversaries in the random oracle model based on the elliptic curve discrete logarithm problem (ECDLP) assumption. The performance analysis and comparison show that the scheme is very efficient in terms of computation and communication overhead.