The adaptive control issue of a class of linear time-varying plants with uniformly bounded but piecewise Lipschitz continuous parameters is considered. A pole-placement control strategy which allows the plant to be with fast varying parameters is employed, under the condition of the number of discontinuities of the plant parameters being small on average. For the case where plant parameters are partially unknown, an indirect adaptive control scheme is developed by combining the controller with an estimator with projection and normalisation. In addition, it is shown theoretically that the closed-loop system is stable in the bounded-input bounded-output sense. A simulation example is also given to show the applicability of the control scheme.