We propose a generalized dynamic composition algorithm of weighted finite state transducers (WFST), which avoids the creation of non-coaccessible paths, performs weight look-ahead and does not impose any constraints to the topology of the WFSTs. Experimental results on Wall Street Journal (WSJ1) 20k-word trigram task show that at 17\% WER (moderately-wide beam width), the decoding time of the proposed approach is about 48\% and 65\% of the other two dynamic composition approaches. In comparison with static composition, at the same level of 17\% WER, we observe a reduction of about 60\% in memory requirement, with an increase of about 60\% in decoding time due to extra overheads for dynamic composition.