This paper is concerned with network-based sampled-data observer design problem for a class of switched linear systems in the finite-time H∞ sense. Outputs sampling and the detection of mode variations are both performed via a clock-driven approach, and networkinduced limitations involving transmission delays and data packet dropouts are also taken into account. Moreover, we introduce a novel multiple Lyapunov-Krasovskii functional, which switches along with the switching signals of the observer. The aforementioned technique can effectively reduce the complexity of the observer design procedures induced by the clock-driven detection scheme of mode variations. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.