The floating ring seal has the ability of minimizing clearance without the rubbing phenomenon. It is often used in the turbo pump units of liquid rocket engines due to its superior leakage performance. The exact prediction of the lock-up position of the floating ring, the leakage performance, and the rotordynamic coefficients of the seal is necessary to evaluate the rotordynamic performance of the turbo pump unit. The governing equations(which are based on the Bulk-flow Model) we solved by the Fast Fourier Transform method. The lock-up position, leakage flow rate, and rotordynamic coefficients are evaluated according to the geometric parameters of the floating ring seal.