A common drawback of most adaptive algorithms developed to treat linear time-varying plants is to assume that plant parameters vary slowly, or that their rapidly varying parts are known a priori. Using ’pseudo-differentiators’ to obtain ’pseudo-derivatives’ of estimated controller parameters, we established an adaptive algorithm which works well even if these limitations are removed. As time-varying structures of plant (or controller) parameters are unknown, these systems are called unstructured ones. We also obtained guidance to choose design parameters to achieve system stability and good system performance by analysis. Finally, computer simulation is given to highlight the performance of our proposed adaptive algorithm for linear unstructured time-varying systems.