To generate a NOON state with a large photon number N , the number of operational steps could be large and the fidelity will decrease rapidly with N . Here we propose a method to generate a new type of quantum entangled states, (|N N 00 + |00N N )/ √ 2 called "double NOON" states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process, i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a consequence, the "double" NOON state creation needs only N +2 operational steps. One application of double NOON states is to get a phase error of 1/(2N ) in phase measurement. In comparison, to achieve the same error, a normal NOON state of the form (|2N, 0 + |0, 2N )/ √ 2 is needed, which requires at least 2N operational steps to prepare by using the existing schemes. Our numerical simulation demonstrates that high-fidelity generation of the double NOON states with N ≤ 10 even for the imperfect devices is feasible with the present circuit QED technique.