In this paper, finite-time bounded sampled-data control problem of switched systems with sector bounded nonlinearity and constant time delay is investigated. During the sampled-data control process, two cases, sampling period with or without switches, are discussed. Mismatching errors cased by the asynchronous switching signal and sampling points, are considered. Different from the qualitative properties of Lyapunov stability, the trajectory upper-bound of switched systems is quantitatively estimated to make it finite-time bounded. Moreover, anti-disturbance capability of switched systems can be measured with finite-time weighted L2-gain of switched systems. The proposed method is verified by numerical simulations.