The present invention relates to a connecting device capable of opening and engaging in dual directions, which includes: a supporter; a corresponding supporter capable of being engaged with the supporter; and two connection bars parallel to each other, each of the connection bars is respectively parallel to the supporter and the corresponding supporter, and two ends of each of the connection bars are respectively pivoted with the supporter and the corresponding supporter thereby allowing the corresponding supporter to be rotated and unfolded towards an end direction of the supporter or to be rotated and unfolded towards an opposite end direction of the supporter so as to form the dual-directional opening operation.