A method and apparatus for smoothing a thick walled portion of a steel pipe produced by pressure-welding two opposite longitudinal edges of an open pipe with a squeeze roll after being subjected to induction heating. Outer and inner reduction rollers pressure sandwiches the thick walled portion from the outer and inner surfaces of the pipe, a support supports the inner reduction roller to be rotatable and containing a water passage for cooling water, a connecting rod connects the support device to a coupler and contains a further water passage for feeding cooling water to the water passage, and an anchor holds the connecting rod. In the a method of producing steel pipes two opposite longitudinal edges of the open pipe are preformed before being subjected to the induction heating and thereafter a thick walled portion is smoothed by the above-described apparatus.