Charging that the Sullivan County Society for the Prevention of Cruelty to Children is a ''sham'' whose only purpose is to make it easy for members to carry guns, the New York State Attorney General said yesterday that his office had filed a lawsuit to dissolve the group.

The Attorney General, Robert Abrams, compared the Sullivan County group with the Richmond County Society for the Prevention of Cruelty to Children, which was dissolved by court order last May.

''Some 60 people did nothing relating to abused children,'' Mr. Abrams said about the Staten Island group. ''They merely joined the S.P.C.C. to be able to carry guns and bypass the requirement of applying for a gun license.'' Targeting Shams

''We're now about to clamp down on another one in Sullivan County,'' Mr. Abrams said. ''We feel it's very important to snuff this out.''

Mr. Abrams made his remarks on the WABC-TV program ''Eyewitness News Conference.''

A telephone call yesterday to the office of the Sullivan County society, in Monticello, was picked up by a woman who said she worked for an answering service and could not provide any further information.

Mr. Abrams said his office was investigating another such group, which he declined to name.

The Legislature authorized the establishment of societies for the prevention of cruelty to children in 1875, before there were government agencies to investigate and prevent child abuse.

The private societies are allowed by state law to confer peace officer status on their members, who might face dangerous situations. This allows the members to obtain and carry firearms without going through the normal permit process, including checks for fingerprints and criminal records.

''Some of these chapters do important work,'' Mr. Abrams said. ''There are 18 entities in New York State. We're now trying to separate the real ones from the ones that are nothing more than sham front operations.'' Inquiry Into One Case

The lawsuit was filed in State Supreme Court in Sullivan County and seeks to dissolve the society, to prevent its president, identified as Louis Ferrara, from granting peace officer status, and to bar members from carrying guns solely on the basis of their membership.

Besides Mr. Ferrara, who is identified as a Brooklyn resident, the suit names 11 other defendants. Six of them live in Brooklyn and the others live in Manhattan, Queens, Staten Island, Glen Cove, L.I., and Central Islip, L.I.

The Sullivan County group was incorporated in 1982 and did not have an office until July 1985, according to the Attorney General's office. It has no administrative or professional staff in the county, the Attorney General's office said, and has received ''no gifts, grants or funding from any foundation, corporation or public agency.''

The society investigated only one complaint of child abuse in the last five years, the Attorney General said.

Earlier this month, Mr. Abrams said, Governor Cuomo signed a law, effective Nov. 1, that requires members of these societies to obtain appropriate licenses before they are allowed to carry handguns.