Proteins are generally classified into four structural classes: all-alpha proteins, all-beta proteins, alpha + beta proteins, and alpha/beta proteins. In this article, a protein is expressed as a vector of 20-dimensional space, in which its 20 components are defined by the composition of its 20 amino acids. Based on this, a new method, the so-called maximum component coefficient method, is proposed for predicting the structural class of a protein according to its amino acid composition. In comparison with the existing methods, the new method yields a higher general accuracy of prediction. Especially for the all-alpha proteins, the rate of correct prediction obtained by the new method is much higher than that by any of the existing methods. For instance, for the 19 all-alpha proteins investigated previously by P.Y. Chou, the rate of correct prediction by means of his method was 84.2%, but the correct rate when predicted with the new method would be 100%! Furthermore, the new method is characterized by an explicable physical picture. This is reflected by the process in which the vector representing a protein to be predicted is decomposed into four component vectors, each of which corresponds to one of the norms of the four protein structural classes.