The invention discloses a recommended system and a method with facing social network for context awareness based on the tensor decomposition, and relates to the field of the data mining and the information retrieval. Firstly, the method makes use of a social network massive data set to collect users and projects and contexts, to pay attention to the list information, to establish an original the user-the project-the context mark matrix, to calculate the users similarity, and to establish a user-user similarity matrix; Secondly, aim at the extreme sparsity of the original mark matrix, a sparse mark matrix is predicated and filled by using the tensor decomposition; Thirdly, aim at a problem that the user similarity matrix is sparse, a sparse user similarity matrix is predicated and filled by using the matrix decomposition; Finally, according to some similar interest tendencies of some similar users in the social network, a social normalization item is taken to optimizing the mark matrix. The method deals with the problem that a traditional predicated mark matrix does not consider that the context information and the relationship between users have an effect on marking. Also, the method deals with an obstruction which is caused by the sparsity of the mark matrix brings to the recommended system, thus the accuracy of the recommended system is improved. The method can be widely applied to the fields of the social network, the electronic commerce and the like.