Bilinear pairing is a fundamental operation that is widely used in cryptographic algorithms (e.g., identity-based cryptographic algorithms) to secure IoT applications. Nonetheless, the time complexity of bilinear pairing is $O(n^3)$, making it a very time-consuming operation, especially for resource-constrained IoT devices. Secure outsourcing of bilinear pairing has been studied in recent years to enable computationally weak devices to securely outsource the bilinear pairing to untrustworthy cloud servers. However, the state-of-art algorithms often require to pre-compute and store some values, which results in storage burden for devices. In the Internet of Things, devices are generally with very limited storage capacity. Thus, the existing algorithms do not fit the IoT well. In this paper, we propose a secure outsourcing algorithm of bilinear pairings, which does not require pre-computations. In the proposed algorithm, the outsourcer side's efficiency is significantly improved compared with executing the original bilinear pairing operation. At the same time, the privacy of the input and output is ensured. Also, we apply the Ethereum blockchain in our outsourcing algorithm to enable fair payments, which ensures that the cloud server gets paid only when he correctly accomplished the outsourced work. The theoretical analysis and experimental results show that the proposed algorithm is efficient and secure.