A four-level entangled quantum refrigeration cycle working with a two-qubit entangled system is proposed in this paper. Based on the first law of quantum thermodynamics and the concept of thermal entanglement, the relation between the quantum entanglement and the several thermodynamic quantities such as the heat transfer, the input work and the coefficient of performance is analyzed. It is found that the isoline of the coefficient of performance is the loop line and it no longer monotonically changes with the ratio of entanglement; in a small exchange constant J the operation region of the refrigerator is c1>c2 and in a larger exchange constant J the operation region of the refrigerator may be c1>c2 or c1c2; the maximal coefficient of performance increases as the exchange constant increases.