This paper presents the design of an HTS magnet for an ultra compact MRI system, potentially for the rapid and early diagnosis of brain trauma. Early diagnosis and therapy stratification can reduce the risk for critically brain ill patients with the use of near patient imaging, and can aid with precision medicine. High temperature superconductors (HTS) have the ability to carry large currents in the cryogen free contrition, which can make the MRI system even smaller and lighter. The design and Genetic Algorithm (GA) optimization were based on the FEM package COMSOL Multiphysics with the LiveLink for MATLAB, together with the GA module in the MATLAB optimization toolbox. The relatively thick HTS tape, ST-12-L from the Shanghai Superconductor Technology ® was chosen and that made more difficulty on optimization process. Genetic Algorithm method improved the optimization performance, and the uniformity achieved 2.36 ppm in a 10 × 10 × 10 cm DSV. Two cases of the end double-pancake were compared. Further sensitivity studies were performed on the homogeneity with its relationship to the magnet length, and the thickness of HTS tape. Index Terms-High temperature superconductor (HTS), Magnetic resonance imaging (MRI), HTS magnet, Genetic Algorithm (GA), Finite element method.