Delays occur frequently in biological, chemical, traortation and electronic systems. Time-delay systems are therefore very important classes of systems. In this thesis, we present a method for finding the solution of linear time-varying delay systems using hybrid of block-pulse functions and Fourier series. The properties of the hybrid of block-pulse functions and Fourier series are presented. The method is based upon expanding various time functions in the system as their truncated hybrid functions. Operational matrices of integration, delay and product are presented and are utilized to reduce the solution of delay systems to the solution of algebraic equations. Illustrative examples are included to demonstrate the efficiency, accuracy and applicability of technique.