An apparatus for injection molding a product having a partly thin portion includes a molding die including a male die and a female die for defining a cavity having a volume larger than a volume of the product. A gate is provided to permit molten resin material from an injection molding machine to be injected into the cavity. A slide block disposed in either the male die or the female die has in cross section a dimension corresponding to a dimension of the thin portion of the product. The slide block is movable between a retracted position where the volume of the cavity is substantially maintained and an advanced position to project into the cavity to form the thin portion. A drive is provided for moving the slide block to the advanced position before the resin material injected into the cavity is solidified. A hollow space formed in the molding die and communicating with the cavity permits an excess of the resin material to be discharged from the cavity into the hollow space during the advance of the slide block. A closure member is fitted in the hollow space for normally closing the same and is coupled to a spring for urging the closure member to the retracted position and a power drive unit for maintaining the closure member in the advanced position against the spring. The closure member is moved in synchronism with the slide block drive so that the closure member is retracted to open the hollow space substantially simultaneously with the advance of the slide block, and is advanced to reduce the volume of the hollow space immediately after the slide block reaches the advanced position. This synchronous drive supplements any shrinkage of the resin during subsequent cooling thereby preventing any occurrence of sink marks in the resulting product.