An apparatus for feeding pasta sheet into a pasta-making machine, includes a feed device for feeding a strip of pasta sheet along a predetermined path, and a punching device designed to operate on the strip in the stop condition so as to punch the strip and obtain from the strip cut pieces of pasta sheet intended to be wrapped around respective portions of filling, thereby producing respective pieces of filled pasta. The apparatus includes a speed variator device for the feed speed of the strip, interposed between the feed device and the punching device for causing, during each machine cycle of the apparatus, a variation in the speed of a branch of the strip positioned at the punching device which, in combination with the speed at which the strip is supplied by the feed device, stops the branch of the strip.