We study a class of KMS-symmetric quantum Markovian semigroups on a quantum spin system ($mathcal{A},{ au},{omega}$), where $mathcal{A}$ is a quasi-local algebra, $ au$ is a strongly continuous one parameter group of *-automorphisms of $mathcal{A}$ and $omega$ is a Gibbs state on $mathcal{A}$. The semigroups can be considered as the extension of semi groups on the nontrivial abelian subalgebra. Let $mathcal{H}$ be a Hilbert space corresponding to the GNS representation con structed from $omega$. Using the general construction method of Dirichlet form developed in [8], we construct the symmetric Markovian semigroup ${T_t}{_t_geq_0}$ on $mathcal{H}$. The semigroup ${T_t}{_t_geq_0}$ acts separately on two subspaces $mathcal{H}_d$ and $mathcal{H}_{od}$ of $mathcal{H}$, where $mathcal{H}_d$ is the diagonal subspace and $mathcal{H}_{od}$ is the off-diagonal subspace, $mathcal{H}=mathcal{H}_d;{igoplus};mathcal{H}_{od}$. The restriction of the semigroup ${T_t}{_t_geq_0}$ on $mathcal{H}_d$ is Glauber dynamics, and for any ${eta}{in}mathcal{H}_{od}$, $T_t{eta}$, decays to zero exponentially fast as t approaches to the infinity.