The passive levitation has a self-adjust characteristic to adapt to environmental changes. Levitation Height (LH) or Lateral Displacements (LD) of the high-temperature superconducting (HTS) Maglev vehicle, running over Permanent Guideway (PMG), will change respectively or synchronously due to some external reasons, which caused the vehicle move a certain distance in vertical direction (Y direction) or horizontal direction (X direction) according to a line space route curve along Y or X direction, or random route lying in a XY plane which is perpendicular to the vehicle running direction (Z direction) corresponding to a complicated space route curve. In these cases, how are the levitation performances of the HTS bulk? From a simplest space line route, this paper studied computationally the curve route levitation performance of the HTS bulk which is subject to a PMG applied field. Results show that the change of the levitation and guidance force is different when the HTS bulk moved along line space route. This provides important scientific theories for the numerical simulation of HTS Maglev vehicle.