  For a local Cohen-Macaulay ring R of finite CM-type, Yoshino has applied
methods of Auslander and Reiten to compute the Grothendieck group of the
category mod(R) of finitely generated R-modules. For the same type of rings we
compute in this paper the first Quillen K-group of mod(R). We also describe the
group homomorphism induced by the inclusion of proj(R) into mod(R) and
illustrate our results with concrete examples.
