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The intelligent reflecting surface (IRS) is considered a core technology of next-generation mobile communication. It has significant advantages in enhancing network coverage, spectrum efficiency, energy efficiency, and deployment cost. Compared with the conventional massive multiple-input-multiple-output (MIMO) system, cell-free massive MIMO overcomes the limitation imposed by inter-cell interference in traditional cellular mobile networks and realizes coherent transmission centered on users. In this article, we consider a new application scenario for the IRS - an aerial IRS (AIRS)-aided cell-free massive MIMO system where multiple APs serve several users through an AIRS. The users are in a “shadow area” where we cannot provide good quality of service (QoS) due to the remote location and the shelter of tall buildings. Our goal is to optimize the power allocation and beamforming of each AP, the placement and reflection phase shift parameters of the AIRS to maximize the user's achievable rate. Firstly, we consider the optimization for fixed placement of the AIRS, where we propose a joint optimization strategy to maximize the achievable rate of the user. Then, we propose a fast optimal location search algorithm base on the path loss model to determine the optimal location of the AIRS and decrease the computational complexity. The simulation results show that the proposed methods can improve the performance for the achievable rate of the system. To the best of our knowledge, this article is the first to study the application scenario for the combination of IRS technology and a cell-free massive MIMO system.