Abstract: Two-phase natural circulation density wave instability under heaving conditions have been studied using PNCMC code（Program for natural circulation under motion condition）. Natural circulation density wave instability still occurred under heaving conditions, and the coupling of heaving motion and density wave instability induced much more complicated oscillation of mass flow rate. The period of complex flow oscillation was one heaving period under heaving with long period（13s, 23s）. However, there were two types of oscillation state under heaving with short period（3s）, for the cases of low heating power, the periodicity of flow oscillation was not significant; for the cases of high heating power, and the periodicity of flow oscillation was very significant. Heaving moved up stability boundary of natural circulation, the smaller the heaving period, the greater the amount of up.