In the MUSES project, kicker magnets are used for the fast extraction of ion-beams. The extraction kicker field is required to rise from approximately 10% to 99% of the full strength of 0.084 T during the time interval between bunches. The high performance of the kicker magnet is important for the efficiency of beam extraction. Based on the traveling-wave-type kicker magnet, we have succeeded in shortening field rise-time and improving the field uniformity. We have measured the magnetic field variation and distribution with a long and short search coils. To measure the field variation accurately, we have used newly devised coaxial-type attenuators instead of a conventional high-voltage probe. In order to improve the signal-to-noise ratio, two signals measured by switching the polarity of the search coil are averaged upon changing the sign. The rise-time of the waveform is approximately 83 ns, and the flat-top time is 888 ns. The uniformity of the magnetic field along the horizontal axis is better than ±0.2% in the range of 85 mm. We have developed a kicker magnet mostly satisfying our requirements for the MUSES project.