  The Liouville Brownian motion which was introduced in \cite{GRV} is a natural
diffusion process associated with a random metric in two dimensional Liouville
quantum gravity. In this paper we construct the Liouville Brownian motion via
Dirichlet form theory. By showing that the Liouville measure is smooth in the
strict sense, the positive continuous additive functional $(F_t)_{t \ge 0}$ of
the Liouville measure in the strict sense w.r.t. the planar Brownian motion
$(B_t)_{t \ge 0}$ is obtained. Then the Liouville Brownian motion can be
defined as a time changed process of the planar Brownian motion $B_{F_t^{-1}}$.
