The paper investigates a distributed optimization algorithm for a class of first-order multi-agent systems with unknown external disturbance. In the distributed optimization task, each agent is only allowed to use its own local cost function and the state information of its neighbors to design a distributed optimization algorithm, so that the global cost function which is the sum of all local cost functions obtains the minimum value. To solve this problem, an active disturbance rejection control distributed optimization algorithm which consists of an extended state observer and an optimization algorithm is proposed. Then, based on the Lyapunov stability, a new method is developed to prove the convergence and stability of the closed-loop system rigidly. When the external disturbance is constant, the designed method can make the states of all agents exponentially converge to the minimum of the global cost function. When the external disturbance is bounded, by adjusting the gain parameter of the extended state observer, the designed method can make the states of all agents converge to an arbitrarily small neighbourhood of the global cost function's minimum value. Finally, the simulation results show the effectiveness of the proposed algorithm.