The theoretic design, the 2-D magnetic field calculation and the electrical calculation of a kicker magnet for CSRm extraction are described as well as the construction design and the manufacture of some key parts. In order to decrease the additional inductance of the magnet, a one-turn coil and ferrite cores are used in the magnet. Each pair of the magnets are powered by a pair of pulse power supplies. The designed inductance is less than 1 μH and the field homogeneity is better than ±0.5% at the peak value of 0.038 T. The magnet meets all of the strict requirements.