  We construct the thermodynamic geometry of $2+1$ dimensional normal (exotic)
BTZ black hole regarding to the fluctuation of cosmological constant. We argue
that while the thermodynamic geometry of black hole without fluctuation of
cosmological constant is a two dimensional flat spaces, the three dimensional
thermodynamics parameters space including the cosmological constant as a
fluctuating parameter will be curved. Some consequence of the fluctuation of
cosmological constant will be investigated. We show that such fluctuation leads
to a thermodynamics curvature which is correctly singular at critical surface
of the system. Also, we consider the validity of first thermodynamics law
regarding to the fluctuation of cosmological constant.
