A new dynamic mesh algorithm is developed in this paper to realize the three-dimensional (3D) computational fluid dynamics (CFD) method for studying the small clearance transient flow field of tilting pad journal bearings (TPJBs). It is based on a structured grid, ensuring that the total number and the topology relationship of the grid nodes remain unchanged during the dynamic mesh updating process. The displacements of the grid nodes can be precisely recalculated at every time step. The updated mesh maintains high quality and is suitable for transient calculation of large journal displacement in FLUENT. The calculation results, such as the static equilibrium position and the dynamic characteristic coefficients, are consistent with the two-dimensional (2D) solution of the Reynolds equation. Furthermore, in the process of transient analysis, under conditions in which the journal is away from the static equilibrium position, evident differences appear between linearized and transient oil film forces, indicating that the nonlinear transient calculation is more suitable for studying the rotor-bearing system.