The adsorption and charge inversion by flexible polyelectrolytes (PEs) onto an oppositely charged spherical surface from a bulk solution of finite PE concentration are studied via numerically solving the coupled ordinary differential equations derived from the continuum self-consistent field (SCF) theory under the ground-state dominance approximation. The effects of various parameters, including the particle radius (r(0)) and its surface charge density (sigma(sf)), PE charge fraction (p), short-range surface-PE inter-action, solvent quality, and bulk PE concentration and salt concentration, on the amount of adsorbed PEs (Gamma) and charge inversion ratio are investigated in detail. It is found that in salt-free solutions where the electrostatic interaction is dominant a relationship of approximate to sigma(sf) (0) (2)/p is generally satisfied. The critical particle radius and its surface charge density for PE adsorption are computed as a function of the bulk salt concentration. It is also found that PE adsorption occurs in most cases, whereas strong charge inversion cannot occur either in salt-free solutions or for nonadsorbing surfaces. For attractive surfaces, increasing the bulk salt concentration, or decreasing the surface charge density and the particle radius, generally enhances the charge inversion. Our results on the charge inversion are consistent with previous SCF calculations for planar and cylindrical surfaces.