Abstract: n this paper, by applying the elemental properties of the block pulse functions to time varying linear systems with quadratic performance index, the time varying LQ optimal control problems are transformed into a particular class of multi-stage dynamic programming problems, By solving the latter, the piece-wise constant solutions to the original problems can be obtained. A new recursive algorithm which is moresimple in form and more convenient for computer is developed. Compared with the methods in references1-3the recursive algorithm obtained here is more simple and explicit , the computational cost and storagespaces of that can be greatly reduced. The recursive algorithm of solution is illustrated by an appropriate example.