Internet giant Google Inc. is considering a plan to offer paid cable-TV services to consumers, a move that could unleash a new wave of competition within the traditional TV business.

Google has looked at ways to expand a previously announced project to build a high-speed Internet service in Kansas City, Mo., and Kansas City, Kan., adding video and phone service in a mirror of offerings from cable and telecom companies, according to people briefed on its plans. As a result, Google has discussed distributing major TV channels...