On basis of a coarse-grained model, we investigate the conformational behavior of a spherical polyelectrolyte brush (SPB) in a solution containing oppositely charged linear polyelectrolytes. Our results obtained from Brownian dynamics (BD) simulations show that with increasing amount of linear polyelectrolytes the SPB undergoes the process of swelling -> collapse -> reswelling. The collapse of the SPB is due to the replacement of confined counterions by linear polyelectrolytes and is well described within a theoretical mean field approach. This replacement and a strong correlation between linear chains and SPB chains lead to a drop in the osmotic pressure inside the SPB. The reswelling is caused by further adsorption of linear chains and counterions. This in turn results in an enhanced excluded volume effect within SPB. A weak charge inversion of the SPB complex is observed. With increasing length of linear polyelectrolytes the collapse of the SPB and its reswelling is shifted toward lower concentrations of linear chains at which both effects occur. An increasing grafting density induces a multilayer structure of adsorbed linear chains and SPB chain segments. The packing process in turn increases the thickness of the SPB. We find that adsorbed linear polyelectrolytes are significantly denatured compared to the free ones in the solution.