$$H_2\overset{-1}{O}_2 +H_2\overset{-1}{O_2}\longrightarrow 2H_2\overset{-2}{O} + \overset{0}{O_2}$$
In this reaction, one molecule of $$H_2O_2$$ is oxidising to $$O_2$$ and another molecule of $$H_2O_2$$ is reduced to $$H_2O$$. So, $$H_2O_2$$ acts as both oxidising and reducing agent.