A structure for connecting a strut bar is provided to reinforce lateral rigidity of an engine room of a vehicle. The structure includes a first strut bar that has a first end coupled to a dash panel of a vehicle and a second end coupled to a strut housing and a second strut bar that has a first end coupled to the dash panel and a second end coupled to the first strut bar, and is disposed to have a predetermined angle with respect to the first strut bar. Further, a connecting bar has a first end coupled to the first strut bar and a second end coupled to the second strut bar, and connects the first strut bar and the second strut bar to increase lateral rigidity of a vehicle body, diversify load paths during a collision, and tune a degree to which the dash panel is pushed.