In this paper, the problem of finite-time boundedness of switched systems in the presence of both discrete and distributed delays is addressed. The multiple Lyapunov–Krasovskii functional approach is proposed to give some criteria ensuring that the state trajectories of the system remain bounded within a finite time interval. The switching law is designed in terms of average dwell time technique and the Jensen inequality. To further reduce the conservatism, we adopt the Wirtinger inequality which encompasses the Jensen one to derive a new condition. Finally, two numerical examples are presented to demonstrate the effectiveness of our result and the potential of employing the Wirtinger inequality.