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Cloud manufacturing (CMfg) is emerging as an advanced service-oriented manufacturing model for the manufacturing industry. It is changing the way manufacturing enterprises organize production activities in that tangible and intangible manufacturing resources encapsulated as virtualized manufacturing services are provided to customers. In this background, CMfg task semantic modeling and description is proposed to address different challenges such as matching with manufacturing services. Firstly, some of the essential features of CMfg tasks are briefly discussed and classification as well as the modeling requirements of CMfg tasks is also investigated, and then this paper proposes the modeling framework of CMfg task to solve the general CMfg task ontology (GCMT_Ontology) construction and the task sub-ontology matching from GCMT_Ontology. In GCMT_Ontology construction process, the original CMfg task ontology (OCMT_Ontology) is built from the CMfg task description model, and then an ontology learning approach is advanced to perfect the GCMT_Ontology with graph-based semantic similarity algorithm. In task sub-ontology matching process, semantic feature values of concepts are calculated to extend the semantic content of the task document, and the extended concepts are input to find the sub-ontology by computing minimum connected sub-graph. Finally, the proposed framework is realized in a prototype system, and an example of cement grinding mill assembling task is carried out in a group enterprise to illustrate the application. The results show that the proposed method improves enterprise collaboration and interoperation effectively. [ABSTRACT FROM AUTHOR]