We apply the gradient-directed Monte Carlo (GDMC) method to select optimal members of a discrete space, the space of chemically viable proteins described by a model Hamiltonian. In contrast to conventional Monte Carlo approaches, our GDMC method uses local property gradients with respect to chemical variables that have discrete values in the actual systems, e.g., residue types in a protein sequence. The local property gradients are obtained from the interpolation of discrete property values, following the linear combination of atomic potentials scheme developed recently [M. Wang et al., J. Am. Chem. Soc. 128, 3228 (2006)]. The local property derivative information directs the search toward the global minima while the Metropolis criterion incorporated in the method overcomes barriers between local minima. Using the simple HP lattice model, we apply the GDMC method to protein sequence design and folding. The GDMC algorithm proves to be particularly efficient, suggesting that this strategy can be extended to other discrete optimization problems in addition to inverse molecular design.