  We discuss the Penner type matrix model recently proposed by Dijkgraaf and
Vafa for a possible explanation of the relation between four-dimensional gauge
theory and Liouville theory by making use of the connection of the matrix model
to two-dimensional CFT. We first consider the relation of gauge couplings
defined in UV and IR regimes of N_f = 4, N = 2 supersymmetric gauge theory
being related as $q_{{\rm UV}}={\vartheta_2(q_{{\rm IR}})^4/\vartheta_3(q_{{\rm
IR}})^4}$. We then use this relation to discuss the action of modular
transformation on the matrix model and determine its spectral curve.
  We also discuss the decoupling of massive flavors from the N_f = 4 matrix
model and derive matrix models describing asymptotically free N = 2 gauge
theories. We find that the Penner type matrix theory reproduces correctly the
standard results of N = 2 supersymmetric gauge theories.
