Short-range and long-range contacts are important in forming protein structure. The proteins can be grouped into four different structural classes according to the content and topology of alpha-helices and beta-strands, and there are all-alpha, all-beta, alpha/beta and alpha+beta proteins. However, there is much difference in statistical property for those classes of proteins. In this paper, we will discuss protein structure in the view of the relative number of long-range (short-range) contacts for each residue. We find the percentage of residues having a large number of long-range contacts in protein is small in all-alpha class of proteins, and large in all-beta class of proteins. However, the percentage of residues is almost the same in alpha/beta and alpha+beta classes of proteins. We calculate the percentage of residues having the number of long-range contacts greater than or equal to (>/=) N(L)=5, and 7 for 428 proteins. The average percentage is 13.3%, 54.8%, 41.4% and 37.0% for all-alpha, all-beta, alpha/beta and alpha+beta classes of proteins with N(L)=5, respectively. With N(L) increasing, the percentage decreases, especially for all-alpha class of proteins. In the meantime, the percentage of residues having the number of short-range contacts greater than or equal to N(S) (>/=N(S)) in protein samples is large for all-alpha class of proteins, and small for all-beta class of proteins, especially for large N(S). We also investigate the ability of amino residues in forming a large number of long-range and short-range contacts. Cys, Val, Ile, Tyr, Trp and Phe can form a large number of long-range contacts easily, and Glu, Lys, Asp, Gln, Arg and Asn can form a large number of long-range contacts, but with difficulty. We also discuss the relative ability in forming short-range contacts for 20 amino residues. Comparison with Fauchere-Pliska hydrophobicity scale and the percentage of residues having large number of long-range contacts is also made. This investigation can provide some insights into the protein structure.