This paper is conced with the H2 estimation and control problems for uncertain discretetime systems with norm-bounded parameter uncertainty. We first present an analysis result on H2 norm bound for a stable uncertain system in terms of linearmatrix inequalities (LMIs). A solution to the robust H2 estimation problem is then derived in terms of two LMIs. As compared tothe existing results, our result on robust H2 estimation is more general. In addition, explicit search of appropriate scaling parametersis not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H2control problem which has been difficult for the traditional Riccati equation approach since no separation principle has been knownfor uncertain systems. The design approach is demonstrated through a simple example.