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This paper considers the robust H2 control problem of continuous-time interval state-space systems. A necessary and sufficient LMI-based condition is derived for analysis of quadratic stability and robust H2 control. Using the analysis result, a state feedback controller and a static output feedback controller can be designed so that the closed-loop interval state-space system is quadratically stable and all its transfer matrices have an H2-norm bounded by a prescribed value. Two LMI-based conditions are derived respectively for the solvability of the above design problems. To the best of the authors' knowledge, the results of robust H2 performance of interval state-space systems is scarce in the literature. This paper seems the first one attempting to deal with robust H2 control analysis and design of interval state-space systems.