Accelerators have been constantly developed widely used in a variety of applications for particle physics, material science, medicine, etc. The accelerator system has several magnets for control the particle trajectory. Among them, a quadruple magnet is employed to focus the accelerated particle beam. In conventionally, the quadruple magnet was made of low temperature superconductors (LTS) and iron carved for specific shape. However, that magnet has a nonlinear magnetic field characteristic with respect to the operating current due to the hysteresis characteristic of the iron core. For this reason, gradient, uniformity and effective length, indicating the performance of a quadruple magnet, are nonlinearly changed with respect to the operating current. Therefore, in order to improve such nonlinear characteristic, we eliminate the iron yoke for design an air-core LTS quadruple magnet. Therefore, we will show the design method and results of the air-core LTS quadruple magnet, and the magnetic field characteristics of air-core magnet will be compared with those of previously designed iron-core quadrupole.