Searchable encryption with advanced query function is an important technique in today's cloud environment. To date, in the public key setting, the best query function supported by the previous schemes are conjunctive or disjunctive keyword search, which are elementary but not enough to satisfy the user's query requirements. In this paper, we make a progress for constructing a searchable public key encryption scheme with advanced query function called simple Boolean keyword search. To create our scheme, we proposed a keywords conversion method that projects the index and query keywords into a group of vectors. Based on a combination of these obtained vectors and an adaptively secure inner product encryption scheme, a public key encryption with simple Boolean keyword search scheme is proposed. We also present both theoretical and experimental analysis to show the effectiveness of this scheme. To the best of our knowledge, it is the first time to give a searchable public key encryption scheme supporting queries like q₁op₁q₂op₂…op_i-1q_iop_i…op_n-1q_n, where op_i is a logical operator which can be and(∨) or or(∧) and q_i is a keyword.