Nowadays, axial flux switching permanent magnet machines are attractive and widely used in direct drive applications because of their unique features. This paper proposes a high temperature superconductor (HTS) disk axial flux switching permanent magnet (AFSPM) machine with spoke type permanent magnets (PMs) and three-phase two layers concentrated windings. The novelty of the proposed machine is using HTS material on the rotor and stator as a disk, insignificant relative permeability of the HTS materials causes magnetic reluctance to become extreme. Because of this feature HTS-Disk in the proposed HTS-AFSPM machine does not allow the flux to enter or exit which causes leakage flux reduces. In order to better investigate and fair comparison, all analyses have done at the same condition using the finite element method (FEM) by Ansys Maxwell. The comparison results show that the proposed HTS-Disk AFSPM machine achieves higher back-EMF, permanent magnet (PM) flux, flux distribution, lower inductance and losses and fewer total harmonics distribution compared to conventional AFSPM machine.