Based on the van Cittert-Zernike theorem, we study the spatial coherence distribution of the light beam, which radiated from the high-power single-color light-emitting diodes (LED) after propagation theoretically. The theoretical calculations show that, the spectral coherence of the light beams which radiated from the non-coherent LED source changed into partially coherent after propagation. Moreover, the spatial coherence of the light beams is related to its chip architecture of the LED. By double-slit interference we measure the spatial coherence of the light beams experimentally. And the visibility of the interference fringes show that the light beams from the non-coherent LED source change into partially coherent after propagation. In addition, the measurement of the visibility by use of adjustable double-slit reveal that, the emitting area of the LED determines the spatial coherence of the light beams from LED source. The theoretical result of the spatial coherence is almost consistent with the experimental measurement.