We derive mean proper motions of 15 known Large Magellanic Cloud (LMC) old globular clusters (GCs) from the Gaia DR2 data sets. When these mean proper motions are gathered with existent radial velocities to compose the GCs’ velocity vectors, we found that the projection of the velocity vectors onto the LMC plane and those perpendicular to it tell us about two distinct kinematical GC populations. Such a distinction becomes clear if the GCs are split at a perpendicular velocity of 10 km/s (absolute value). The two different kinematics groups also exhibit different spatial distributions. Those with smaller vertical velocities are part of the LMC disk, while those with larger values are closely distributed like a spheroidal component. Since GCs in both kinematic-structural components share similar ages and metallicities, we speculate with the possibility that their origins could have occurred through a fast collapse that formed halo and disk concurrently.