************************************************************************* 61111 We propose a X-ray spectroscopic observation of a Wolf-Rayet (W-R) starburst galaxy Mrk 1259 in order to search for the hard X-ray emission from AGN and to investigate the properties of the hot plasma. Previous optical studies on W-R galaxies indicate that the star- formation activities in starburst galaxies occur instantaneously with the duration time of less than 1e6 years. Thus, by selecting W-R galaxies, we can study the early phase of the star-formation. We search for the hard X-ray emission which, if present, would provide evidence for the Warmer (Terlevich and Mernick 1985). We also analyze the temperature and metallicity of the hot plasma to study their evolutionary change during the starburst activity by comparing with normal starburst galaxies. *************************************************************************