A cover opening device of an electric sunshade for a side window is provided for connecting between a base and a protecting cover of the electric sunshade and connecting with a curtain support rod. The cover opening device operates by the curtain support rod mounted with a driving element passing through a pedestal, a linkage rod part connected with an abutted part connecting with the protecting cover to move the abutted part downward by a press of the driving element and to pivot the protecting cover for covering a groove by the linkage rod part, and an elastic element providing resilience force for opening the protecting cover. The cover opening device has a mechanism that opens the protecting cover beforehand and closes the protecting cover afterwards, thereby preventing the curtain from colliding with the protecting cover when the curtain is extending out and rolling up.