Aiming to improve the cleaning performance of maize grain harvester cleaning device under the condition of large feeding mass, a multi-tetragonal conical sieve was designed to make the maize grains on the sieve retained and quickly penetrate the sieve through the non-planar structure. The key structural parameters of the multi-tetragonal conical sieve were determined by theoretical analysis. CFD-DEM method was used for numerical simulating the motion of gas-solid two-phase in multi-tetragonal conical sieve cleaning device. A high speed airflow belt could be formed in front of the multi-tetragonal conical sieve, which was beneficial to make maize mixtures separated. The air velocity in the middle of the sieve body was low, which was conducive to the retention of maize grain with the structure of multi-tetragonal conical sieve. The maize grain on the sieve completed the process of ‘impact sieve-retention-leaping-impact sieve-through the sieve’ under the movement of multi-tetragonal conical sieve. No build-up of the maize mixture on the sieve. The maize grain on the sieve completed rapid penetration of the sieve. The height of multi-tetragonal conical sieve unit, the airflow velocity at the inlet of the cleaning device and the vibrating amplitude of the vibrating sieve were selected as the test factors. The impurity rate, loss rate and screening efficiency of maize grain were selected as test indexes. The quadratic orthogonal rotation combination test was carried out. The mathematical models between factors and indicators were established. The best combination of parameters was obtained as follows, the height of the multi-tetragonal conical sieve unit was 11.26mm, the airflow velocity of the cleaning device was 9.6m/s, the vibration amplitude of the vibrating screen was 15.13mm. The motion law of maize grains on the sieve was verified through the bench validation test. At the maize mixture feeding mass of 7kg/s, the impurity rate of maize grain after screening by the multi-tetragonal conical sieve cleaning device was 1.68%, the loss rate of maize grain was 1.33%, and the screening efficiency of maize grain was 3.66kg/s. The multi-tetragonal conical sieve cleaning device could meet the requirements of cleaning maize mixtures with large feed mass. The research result had a certain reference value for improving the working performance of maize grain combine harvester.