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We numerically investigate the radiation forces of multi-Gaussian Schell-model (MGSM) beams, in which the degree of coherence is modeled by the multi-Gaussian function, exerted on the Rayleigh dielectric sphere. By simulation of the forces calculation it is found that the steepness of the edge of the intensity profile (i.e., the summation index M) and the initial coherence width of the MGSM beams play important roles in the trapping range and stability. We can increase the trapping range at the focal plane by increasing the value of M or decreasing the initial coherence of the MGSM beams. It is also found that the trapping stability becomes lower due to the increase of the value of M or the decrease of coherence. Furthermore, the trapping stability under different conditions is explicitly analyzed. The results presented here are helpful for some possible applications.