We study a class of KMS-symmetric quantum Markovian semigroups on a quantum spin system (

), where

is a quasi-local algebra,

is a strongly continuous one parameter group of *-automorphisms of

and

is a Gibbs state on

. The semigroups can be considered as the extension of semi groups on the nontrivial abelian subalgebra. Let

be a Hilbert space corresponding to the GNS representation con structed from

. Using the general construction method of Dirichlet form developed in [8], we construct the symmetric Markovian semigroup

on

. The semigroup

acts separately on two subspaces

and

of

, where

is the diagonal subspace and

is the off-diagonal subspace,

. The restriction of the semigroup

on

is Glauber dynamics, and for any

,

, decays to zero exponentially fast as t approaches to the infinity.