Beam dynamics of the racetrack-shape fixed field induction accelerator for giant cluster ions were established. Linear optics theory and Runge-Kutta particle tracking approaches were developed, and the consistency between two approaches was confirmed. Use of gradient field bending magnets with a reverse field strip and ramping quadrupole doublets were crucial to achieve the orbit stability. A physically limited size of the huge bending magnet in the longitudinal direction generated the inherent closed-orbit distortion that substantially affected the orbit stability. In addition, the inherent field component ${B}_{s}$ along the orbit coordinate ``$s$'' induced horizontal-vertical (H-V) couplings. A possible correction method of this closed-orbit distortion was proposed. A net effect of the H-V coupling was evaluated. Longitudinal motion with a time-varying transition energy, which is one of characteristic features in the racetrack-shape fixed field induction accelerator, was studied with the help of computer simulations.