The complexation between a linear flexible polyelectrolyte and one or several oppositely charged macroions was examined by employing a simple model system with focus on the electrostatic interactions. The composition and the structure of the complex as well as conformational data of the polyelectrolyte were obtained by using Monte Carlo simulations. These properties were investigated at different linear charge densities of the polyelectrolyte, different chain lengths of the polyelectrolyte, and different macroion charges, all at different numbers of macroions at constant volume. The binding isotherms obtained are Langmuir type, and in excess of macroions the polyelectrolyte-macroion complex displays a charge reversal. Upon complexation, the polyelectrolyte extension first reduces and thereafter increases as the number of complexed macroions increases, the minimal extension appearing for a neutral complex. Macroions prefer to complex to central polyelectrolyte segments, but for a neutral or an overcharged complex the entire polyelectrolyte chain is involved. In the complex, the macroions are able to come into direct contact with each other, despite their mutual electrostatic repulsion. The distribution of the small ions is also presented.