Lysozyme adsorption to charged surfaces was studied by Monte Carlo simulations at different protein concentrations, protein net charges, ionic strengths, and surface charge densities. The lysozyme was represented by a hard sphere with embedded positive and negative surface charges parametrically dependent on the solution pH. A short-range attractive protein-protein potential was included to represent attractive non-Coulomb forces. The charged surface was described by a hard wall with embedded charges representing a mica surface. The protein adsorption was favored by high protein concentration, high protein net charge, low ionic strength, and high surface charge density. Nevertheless, adsorption appeared also for a weakly negatively charged protein to the negatively charged surface as a result of an electrostatically favorable protein orientation at the surface. While a multipole expansion including monopole and dipole moments only was insufficient to explain preferential orientation, an expansion including also quadrupole moments provided a satisfactory picture. Finally, it was found that the short-range attraction between the proteins increased the adsorbed amount, as well as the structure in the adsorbed protein layer. The adsorbed amounts obtained compared favorably with experimental results.