Abstract: The microlocalized properties of a module over a filtered ring R are discussed by many papers in recent years.For example,Essen proved that if M is a module with regular singularities over a Zariski ring R,then its microlocalization Q\+μ\-S(M) is a Q\+μ\-S(R) module with regular singularities.But it is unknown that if Q\+μ\-S(M) is a R module with regular singularities.In this paper the regular singularities of the microlocalization Q\+μ\-S(M) are discussed as an R module while R is a Zariski filtered ring and M is an R module with regular singularities.An answer to the problem in suitable conditions is given.The result is proved that if M is a R module with regular singularities and the localized filtation on M is a good R filtration then the microlocalization Q\+μ\-S(M) of M is a R module with regular singularities.