Weighted Directed Word Graph is a new text-indexing structure which is based on a new compaction method on DAWG. WDWGs are basically cyclic, means that they may accept infinite strings. But by assigning weights to the edges, the acceptable strings are limited only to the substrings of input strings. The size of WDWGs is smaller than that of DAWGs both in theory and practice. A linear-time on-line construction algorithm for WDWGs is also presented.