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We present an experimental determination on the Landé g-factors for the 5s2 1S0 and 5s5p 3P0 states in ultra-cold atomic systems,which is important for evaluating the Zeeman shift of the clock transition in the 87Sr optical lattice clock.The Zeeman shift of the 5s5p 3P0-5s2 1S0 forbidden transition is measured with the π-polarized and σ±-polarized interrogations at different magnetic field strengths.Moreover,in the g-factor measurement with the σ±-transition spectra,it is unnecessary to calibrate the exteal magnetic field.By this means,the ground state 5s2 1S0 g-factor for the 87Sr atom is-1.306(52) × 10-4,which is the first experimental determination to the best of our knowledge,and the result matches very well with the theoretical estimation.The differential g-factor δg between the 5s5p 3P0 state and the 5s2 1S0 state of the 87Sr atoms is measured in the experiment as well,which are-7.67(36) × 10-5 with π-transition spectra and-7.72(43) × 10-5 with σ±-transition spectra,in good agreement with the previous report [Phys.Rev.A 76 (2007) 022510].This work can also be used for determining the differential g-factor of the clock states for the optical clocks based on other atoms.