SOPA would empower the Justice Department and copyright holders to demand that search engines, Internet providers and ad networks block access to sites "dedicated" to copyright infringement.
The legislation is aimed at shutting down foreign sites such as The Pirate Bay that offer illegal copies of movies, music and television shows with impunity.
A broad coalition, including the U.S. Chamber of Commerce, Hollywood, the recording industry and organized labor, strongly back the bill.
But consumer groups and major Web companies, including Google, Yahoo and Facebook, warn SOPA could stifle innovation and censor free speech.
The Globe editorial dismissed those concerns.
"While opponents of the bill cry censorship, their fears seem to based on the belief that it somehow creates a slippery slope — that blocking an illegal download of an Adele album will be logically followed by blocking a search for information about the Arab Spring," the editorial board wrote. "The government already has cracked down on online child pornography without a corresponding attack on civil liberties. There’s no reason that the First Amendment would be endangered if the Justice Department beefed up its enforcement of copyright law as well."
The Boston Globe is owned by The New York Times, which came out against the bill in a November editorial.
The House Judiciary Committee is expected to vote on SOPA when Congress returns later this month, and the Senate is set to vote on its version of the bill, the Protect IP Act.