Abstract: In this work, we propose a new concept of a high gradient trapped field magnet (HG-TFM). The HG-TFM is made from (RE)BaCuO bulk superconductors, in which slit ring bulks (slit-TFMs) are tightly stacked with TFM cylinders (full-TFMs), and state-of-the-art numerical simulations were used to investigate the magnetic and mechanical properties in detail during and after magnetization. A maximum value of the magnetic field gradient product of Bz⋅dBz/dz = 6040 T2 m−1 was obtained after conventional field cooled magnetization (FCM) with an applied field, B app, of 10 T of the HG-TFM with 60 mm in outer diameter and 10 mm in inner diameter. This value may be the highest value ever reported compared to any other magnetic sources. The Bz⋅dBz/dz value increased with decreasing inner diameter of the HG-TFM and with increasing B app during FCM. The electromagnetic stress in the HG-TFM during the FCM process mainly results from the hoop stress along the circumferential direction. The simulations suggested that there is no fracture risk of the bulk components during FCM from 10 T in a proposed realistic configuration of the HG-TFM where both TFM parts are mounted in Al-alloy rings and the whole HG-TFM is encapsulated in a steel capsule. A quasi-zero gravity space can be realized in the HG-TFM with a high Bz⋅dBz/dz value in an open space outside the vacuum chamber. The HG-TFM device can act as a compact and cryogen-free desktop-type magnetic source to provide a large magnetic force and could be useful in a number of life/medical science applications, such as protein crystallization and cell culture.