This paper is concerned with the finite-time H∞ control problem for a class of uncertain switched linear neutral systems with time-varying delays. By fully exploiting the mode-dependency of the proposed Lyapunov-Krasovskii functionals, the considered systems could be further investigated with stable and unstable subsystems being concurrently contained. Sufficient criteria are first derived for ensuring finite-time boundedness of the underlying system with a given maximum ratio of activation time between unstable subsystems and stable ones. Then the H∞ performance analysis and the memory state-feedback controller design are carried out for a given performance index. Finally, two numerical examples are presented to illustrate the potential and advantages of the developed findings.