The evolution of entangled decoherence of coupling superconducting qubits in non-Markovian environment is investigated in detail using concurrence function. The results show that, for coupling superconducting qubit under different entangled initial states, because of the role of memory feedback due to environmental effect, the entanglement of coupling superconducting qubits under a thermal bath always tends to zero monotonically. Further results also showed that, the sudden death of entanglement will soon occur in non-Markovian process, stronger the dissipation, faster the death of entanglement. But in Markovian process, it tends to death of entanglement slowly.