The industrial Internet of Things is flourishing, which is unprecedentedly driven by the rapid development of wireless sensor networks (WSNs) with the assistance of cloud computing. The new wave of technology will give rise to new risks to cyber security, particularly the data confidentiality in cloud-assisted WSNs (CWSNs). Searchable public-key encryption (SPE) is a promising method to address this problem. In theory, it allows sensors to upload public-key ciphertexts to the cloud, and the owner of these sensors can securely delegate a keyword search to the cloud and retrieve the intended data while maintaining data confidentiality. However, all existing and semantically secure SPE schemes have expensive costs in terms of generating ciphertexts and searching keywords. Hence, this paper proposes a lightweight SPE (LSPE) scheme with semantic security for CWSNs. LSPE reduces a large number of the computation-intensive operations that are adopted in previous works; thus, LSPE has search performance close to that of some practical searchable symmetric encryption schemes. In addition, LSPE saves considerable time and energy costs of sensors for generating ciphertexts. Finally, we experimentally test LSPE and compare the results with some previous works to quantitatively demonstrate the above advantages.