Distributed quantum computing (DQC) offers a promising approach to overcome resource limitations in the Noisy Intermediate-Scale Quantum (NISQ) era. Multi-objective search problem means searching for any one of several objectives in an unstructured database. Grover’s algorithm provides a quadratic speedup over classical algorithms in multi-objective search problem. The iterated operator in Grover’s algorithm is a key element and plays an important role in amplitude amplification. In this paper, we design a distributed iterated operator and therefore a distributed multi-objective quantum search algorithm is obtained. Compared to Grover’s algorithm, our algorithm requires fewer qubits.