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Although FL is considered privacy-preserved by design, recent data reconstruction attacks demonstrate that an attacker can recover clients' training data based on the parameters shared in FL. However, most existing methods fail to attack the most widely used horizontal Federated Averaging (FedAvg) scenario, where clients share model parameters after multiple local training steps. To tackle this issue, we propose an interpolation-based approximation method, which makes attacking FedAvg scenarios feasible by generating the intermediate model updates of the clients' local training processes. Then, we design a layer-wise weighted loss function to improve the data quality of reconstruction. 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To tackle this issue, we propose an interpolation-based approximation method, which makes attacking FedAvg scenarios feasible by generating the intermediate model updates of the clients' local training processes. Then, we design a layer-wise weighted loss function to improve the data quality of reconstruction. 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