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This paper presents a novel framework of distributed learning model predictive control (DLMPC) for multi-agent systems performing iterative tasks. The framework adopts a non-cooperative strategy in that each agent aims at optimizing its own objective. Local state and input trajectories from previous iterations are collected and used to recursively construct a time-varying safe set and terminal cost function. In this way, each subsystem is able to iteratively improve its control performance and ensure feasibility and stability in every iterations. No communication among subsystems is required during online control. Simulation on a benchmark example shows the efficacy of the proposed method.