Hillocks on N-face GaN (0001) films are effectively eliminated by group-III-source flow-rate modulation epitaxy (FME), wherein the flow-rate of group-III sources are sequentially modulated under a constant supply of NH3. A hillock-free smooth surface obtained by group-III-source FME is attributed to the enhancement of step-flow growth. We found that a hillock originates from a micropipe and grows by spiral growth around the micropipe. The spiral growth rate rapidly decreases with decreasing the degree of surface supersaturation sigma, while the step-flow growth rate decreases linearly. For group-III-source FME, wherein s is lower than conventional continuous growth, the spiral growth rate could be lower than the step-flow growth one so that the formation of hillocks is suppressed.