Our study indicates that the number of trapped Rb atoms in a magneto-optical trap (MOT) strongly depends on the trapping laser intensity and detuning, the repumping laser intensity and the magnetic gradient. We estimate the trapped-atom numbers changing with the trapping laser intensity and detuning, using a two-level system model. The theoretical results are in qualitative agreement with the experimental results. The experimental results also show an obvious dependence of the trapped-atom numbers on repumping laser intensity and the magnetic gradient, which the simple theory cannot account for. These studies are helpful for selecting suitable experimental parameters to achieve larger numbers of cold atoms.