One of the first physics results that CMS will hopefully obtain will be the analysis of heavy quarkonium productions, including the γ cross-section measurement. Since the γ production cross-section from p-p collisions is expected to be relatively large, the analysis should be viable with rather small datasets which will be available soon after the start-up of the LHC. This paper describes the methods and plans for measuring the differential cross-section of γ(1S) →μ+μ- production, by using data to be collected from the CMS detector in the first LHC run. In this study, about 80 thousand T are reconstructed corresponding to an integrated luminosity of 6.4 pb-1 in 10 TeV proton-proton collisions by using Monte Carlo data. The precision of this measurement is estimated to be about 16%, which is limited by the systematic errors.