Abstract: Marine nuclear power platform is one of the main topic research in the field of nuclear energy due to its outstanding safety, but the thermal-hydraulic characteristics are influenced when primary loop and non-inertial conditions operate in natural circulation. Aiming to this problem, several typical primary loop systems were designed to calculate and analyze flow fluctuation characteristics in rolling motion on natural circulation. The scheme designs of double-loop, three-loop and four-loop system models were established respectively. And the position of the rolling center was considered at the same time. According to the momentum conservation equation, the change law of flow was obtained in different states. Flow fluctuation ranges of the loop are 13.2%/11.2%/9.5%, and flow fluctuation ranges of the reactor core are 0.9%/0.8%/0.6% in the double-loop respectively when rolling center is in upper/middle/lower part. Flow fluctuation ranges of the loop and the reactor core are 9.2% and 0.8% respectively in the three-loop when rolling center is in lower part of the ship. Flow fluctuation ranges of the loop and the core are 9.5% and 0.9% respectively for scheme design 1, and 9.2% and 0.7% respectively for scheme design 2 in four-loop. The design scheme with double-loop is most beneficial to the stability of the system.