Regarding the decoherence phenomena caused by some factors of external environment in an open quantum system, a quantum prisoner dilemma game model is established under amplitude channels by using EWL quantization scheme based on quantum game theory. The payoffs and Nash equilibrium solutions are obtained both in memoryless and complete memory channels, and the influence of noise strength on Nash equilibrium is also analyzed. It is found that noise has no effect on Nash equilibrium when the noise strength is less than 0.5961 under the memoryless amplitude damping channel, while the threshold value increases to 0.9654 under the complete memory condition. It indicates that the Nash equilibrium under the complete memory tends to be more stable and less susceptible to the influence of external environment than that under the memoryless condition, which provides a certain reference for decision-making of a feasible solution to the prisoner’s dilemma in the open quantum system.