  In this paper, we holographically study the renormalization group (RG) flow
in a three-dimensional Einstein-dilaton gravity with a potential permitting
several types of the RG flow with nontrivial beta-functions. By using the
intrinsic parameter of the potential, we classify possible holographic RG flows
and examine their physical features. Using the Ryu-Takayanagi formulation,
furthermore, we investigate how the $c$-function of the entanglement entropy
behaves along the RG flow numerically. We show that the entanglement
$c$-function monotonically decreases even in the cases with a nontrivial
beta-function. For checking the consistency, we also compare the result of the
entanglement entropy with the $c$-function derived from the holographic
renormalization procedure.
