We propose novel prediction schemes for protein 3D structure prediction that include both local and global factors of protein structure formation. We have developed a powerful description scheme for protein conformation, MLD (Multi-Level Description), in order to model the protein structure formation. In this scheme, the description is reconstructable into the three-dimensional conformation with a tolerable error. The MLD scheme facilitates the modeling of 1) the relation between the local conformation and the primary structure at that region at various scales (i.e., primary constraints), and 2) the geometric constraints between the neighboring local conformations. Hence, in our prediction schemes, the problem of protein 3D structure prediction is formulated as a combinatorial optimization problem; the 3D conformation of a protein is predicted as the optimal MLD that satisfies most of the constraints. We implemented several schemes to solve this problem. We proved that the degree of prediction accuracy is much improved by introducing the geometric constraints.