A support structure for a car safety seat for installation on an extensible and retractable stroller includes a front frame, a rear frame, a handle grip and a support frame. The support structure includes a first and a second support member mounted on the support frame for supporting the weight of a car safety seat. The first support member is stationary. The second support member has two ends engaged respectively with first and second rotary disks which are turnable about the same axis and which maintain a fixed distance with the first support member. By turning the second support member, the relative distance between the first and second support member may change thereby to support car safety seats of different sizes.