Polymer chains anchored with one end at a hard wall under variable solvent conditions are investigated by Monte Carlo simulations using the bond- fluctuation model. Detail information on the structural properties are obtained above, at, and below the THETA-point and discussed in terms of the appropriate theories. In particular, the scaling of the brush thickness is formulated and verified by the simulation data. For the dynamics at the THETA-point, both the relaxation time of the chain configuration and the mean-quare time displacement are studied. At temperatures distinctly below the THETA-point, we find that the layer develops considerable lateral inhomogeneity in its density, which has not been predicted by previous theories.