Aimed at the problem that the current functional encryption schemes fail to be greatly used the parallel computation ability in the cloud to process large amounts of data, a functional encryption scheme for parallel random access machine is proposed. The scheme allows the data owner to transmit encrypted data once, and authorizes the cloud provider to run parallel algorithm on it. Taking the parallel garbled RAM scheme as a black box, the scheme parallels RAM program hardwired into a circuit, the circuit FE scheme, thus converting any such functional encryption scheme for circuits into a functional encryption for PRAMs. Through the theory analysis, the scheme accomplishes the functional encryption with only poly overhead in the (parallel) running time, and its indistinguishability security is given.