Recently, the deployment of sensors and actuators to collect and disseminate data in various applications such as e-healthcare, vehicular adhoc networks (VANETs) and smart factories has revolutionized several new communication technologies. The Internet of Things (IoT) is one of those emerging communication technologies. These revolutionary applications of IoT in industrial environment are termed as Industry 4.0 and it has vitalized the concept of Industrial IoT (IIoT). Being wireless communication, the authentication and integrity of data are the most important challenges. To mitigate these challenges, several digital signature schemes are proposed in the literature. However, due to identity-based or certificate-less construction, those schemes suffer from inborn key escrow and secret key distribution problems. To resolve such issues, the first certificate-based proxy signature (PFCBPS) scheme without pairing is proposed. The proposed PFCBPS scheme is provably secure in random oracle model (ROM). The performance comparison (in terms of computational costs of different phases and length of resulting delegation and signature) shows that the proposed PFCBPS scheme’s total computational cost is 46.69 ms which is 52.24% of He et al. [8], 61.40% of Debiao et al. [5], 23.33% of Seo et al. [20], 28% of Hu et al. [9] and 36.84% of Verma and Singh [23]. Thus, it is more suitable to IIoT environment than existing competitive schemes.