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In order to solve the problem that the importance of the user's attribute is seldom considered in the most of the existing attribute-based encryption schemes with traitor tracing, we designed a traceable and weighted attribute-based encryption scheme. In our constructed scheme, the private key of the user consisting of user's identity information is applied to trace traitors. In addition, the idea of weighted attribute is introduced, and the attributes set is transformed into the segmentation set of weighted attributes through the attributes set segmentation algorithm. Via employing a linear secret sharing scheme, the constructed scheme offers fine-grained and nimble access control mechanism. Under the assumption of q-BDHE in the standard model, we prove that the designed scheme is able to reach security against chosen-plaintext attack. By comparing with other relevant schemes, it has significant improvement in the costs of communication and computation, and it is more suitable for the application of the mobile terminal in cloud computing.