Due to the big data blowout from the Internet of Things (IoT) and the rapid development of cloud computing, outsourcing computation has received considerable attention recently. Particularly, many outsourcing computation schemes have been proposed to dedicate the outsourcing polynomial computation due to its use in numerous fields, such as data analysis. However, none of them are practical enough, as they either require some time-consuming cryptographic operations to achieve fairness between the user and worker, or cannot allow the user to outsource arbitrary polynomial to the worker, or need two non-collusive workers. To tackle these challenges, we propose a new outsourcing polynomial computation scheme by employing a variant of Horners method and the blockchain technology. Specifically, the former makes the computational cost on the worker side as low as possible, and the latter guarantees the fairness between the user and worker if the computing result can be publicly verified. To achieve the public verifiability property, we apply the sampling technique, which is effective in our proposal according to a game-theoretic analysis. Furthermore, we implement a prototype of our proposal and run it on an Ethereum test net. The experimental results demonstrate that our proposal is efficient in terms of computational cost.