  We study the quantum properties of the three-dimensional higher derivative
gravity. In particular we calculate the running of the gravitational and
cosmological constants. The flow of these couplings shows that there exist both
Gaussian and nontrivial fixed points in the theory, thus confirming that the
theory is asymptotically safe. It is shown that the new massive gravity or
$f(R)$ gravity in three dimensions do not correspond to the fixed point within
the approximation that the coefficients of the higher curvature terms are not
subject to the flow. The fixed point value of the cosmological constant is
found to be gauge-independent, positive and small. We also find that if we
start with Einstein term with negative sign, the fixed point only exists when
the coefficient of the Einstein term has positive sign.
