In a natural language processing system, a large amount of ambiguity and a large branching factor are hindering factors in obtaining the desired analysis for a given sentence in a short time. In this paper, we are proposing a sequential truncation parsing algorithm to reduce the searching space and thus lowering the parsing time. The algorithm is based on a score function which takes the advantages of probabilistic characteristics of syntactic information in the sentences. A preliminary test on this algorithm was conducted with a special version of our machine translation system, the ARCHTRAN, and an encouraging result was observed.