Most of existing CP-ABE (ciphertext-policy attribute-based encryption) schemes have such problems as over-computation and a long calculation time in decryption, which make them difficult to be applied and implemented. To solve this problem, the computation outsourcing is introduced into the design of CP-ABE scheme, a Spark-platform-based CP-ABE scheme with fast decryption for public cloud is proposed. In this scheme, the decryption parallelization algorithm is designed based on the decryption feature of CP-ABE, with which, decryption at both leaf node and root node with over-computation is parallelized. Then, the parallelization tasks are handed over to the Spark cluster. The computation outsourcing makes the most decryption computation done by cloud servers, while the user client only needs an exponential operation, and parallelization greatly improves the speed of decryption. Security analysis shows that the proposed scheme can fight against chosen plaintext attack under both the generic group model and the random oracle model.