Disclosed herein is a damping coupler of an electronic steering apparatus. The damping coupler includes a first spline having a first shaft hole such that a worm shaft is inserted therein, with a first serration being formed in the first shaft hole to engage with a serration of the worm shaft; a second spline coupled to a side of the first spline, and having a second shaft hole such that the worm shaft is inserted therein, with a second serration being formed in the second shaft hole to engage with a serration of the worm shaft; and a molding surrounding outsides of the first and second splines, and coupled to a motor shaft.