The X-ray spectrum of the Coma galaxy cluster was studied using the data from the XMM-Newton observatory. We combined 7 observations performed with the MOS camera of XMM-Newton in the 40'x 40' region centered at the Coma cluster. The analyzed observations were performed in 2000-2005 and have a total duration of 196 ksec. We focus on the analysis of the MOS camera spectra due to their lower affection by strong instrumental line-like background. The obtained spectrum was fitted with a model including contributions from the Solar system/Milky Way hot plasma and a power law X-ray background. The contribution of the instrumental background was modeled as a power law (not convolved with the effective area) and a number of Gaussian lines. The contribution from the Coma cluster was modeled with a single-temperature hot plasma emission. In addition, we searched for possible non-thermal radiation present in the vicinity of the center of the Coma cluster, originating e.g. from synchrotron emission of relativistic electrons on a turbulent magnetic field. We compared the results with previous works by other authors and spectra obtained from other instruments that operate in the similar energy range of 1-10 keV. Careful and detailed spectrum analysis shall be a necessary contribution to our future work - searching for axion-like particles' manifestations in the Coma cluster.