A numerical analysis has been conducted to investigate a modified floating-zone crystal growth process in which most of the melt surface is covered with a heated ring. The crystal rod is not only pulled downward but rotated around its axisymmetric line during crystal growth process in order to produce the flat interface of crystal growth and the single crystal growth of NaNO3 is considered in 6mm diameter. The present study is made from a full-equation-based analysis considering a pulling velocity in all of solid and liquid domains and both of solid-liquid interfaces are tracked simultaneously with a governing equation in each domain. Numerical results are mainly presented for the comparison of the surface shape of rotational crystal rod with that of no-rotational crystal rod and the effects of revolution speeds of the crystal rod. Results show that the rotation of crystal rod produces more its flat surface. In addition, the shape of crystal growth near the centerline is more concaved with the increase in the revolution speed of crystal rod. The flow pattern and temperature distribution is analyzed and presented in each case. As the pulling velocity of crystal rod is increasing, the free surface of the melt below the heated ring is enlarged due to the crystal interface migrating downward.