The invention discloses a straight rotary linkage core puller for an injection mold of an elbow product, comprising a recurved loose core (1), a connecting bar (2), a straight inside loose core (3), a straight outside loose core (4), an inclined guide slider (5), a lag bar (6) and an inclined guide pillar (7). The invention utilizes the technical scheme that the rotary core puller composed of therecurved loose core, the connecting bar, the straight inside loose core and the straight outside loose core is adopted, the straight inside loose core and the straight outside loose core are straightly pulled out in a segmentation mode successively by the inclined guide slider and the lag bar, and the connecting bar pulls the recurved loose core to pull cores rotatably, thus overcoming the problems and shortcomings of flanging on the outer walls of the product, much occupied labor, large working strength, low efficiency, high cost and latent accident potential in the prior art. By the provided straight rotary linkage core puller for the injection mold of the elbow product, automatic core pulling and demolding of the injection molding of the elbow product can be realized, thus achieving the purposes of removing flanging on the outer walls, reducing labor, lightening working strength, improving the production efficiency, lowering the cost and eliminating the accident potential.