Searchable encryption enables users to search over encrypted data without revealing original data. The public key encryption with keyword search (PEKS) is a construction of searchable encryption proposed by Boneh et al. using a public key system. In this paper, we investigate Boneh et al's PEKS construction under the case of full text search, and We design a new index structure which can accelerate the search procedure with a large keywords amount. We also analyze the security of the new construction in the random oracle model.