In this paper, we prepared miniature fuse fabricated with carbon nanotube (CNT) fiber for the use of low rated current under 1 A and high speed operation under 4ms. CNT fuses were fabricated in the form of universal modular fuse (UMF) with different diameter of CNT fibers defined by multiplying the CNT threads. Electrical properties of the CNT fuses were measured such as resistance, rated current, and operation time with current. Resistance of the CNT fuse decreased and rated current increased with the diameter of the CNT fuses, respectively. Consequently, the operation time with current increased with the diameter of the CNT fuses. The CNT fuses fabricated in this work had broad range of low rated current from 0.05 to 1.25 A by multiplying the CNT threads. Operation time was measured about 3.6ms which was applicable to the UMF.