A fast likelihood computation approach called dynamic Gaussian selection (DGS) is proposed for HMM-based continuous speech recognition. DGS approach is a one-pass search technique which generates a dynamic shortlist of Gaussians for each state during the procedure of likelihood computation. The shortlist consists of the Gaussians which make prominent contribution to the likelihood. In principle, DGS is an extension of the technique of Partial Distance Elimination, and it requires almost no additional memory for the storage of Gaussian shortlists. DGS algorithm has been implemented by modifying the likelihood computation module in HTK 3.4 system. Results from experiments on TIMIT and HIWIRE corpora indicate that this approach can speed up the likelihood computation significantly without introducing apparent additional recognition error.