The continuous improvement of information technology will inevitably promote the arrival of the era of big data.Cloud computing provides a powerful data processing platform for big data.However,data security and privacy issues have aroused great concern.In this paper,we propose a new certificateless public key encryption scheme with multiple keywords search and free of secure channel for big data.We also prove that the proposed scheme can resist chosen keyword attack in random oracle model.The performance analysis shows that,the proposed scheme reduces the computation cost as well as the communication cost compared with the scheme proposed by Peng et al.in 2014.