We present in this paper a dynamic programming parsing algorithm in the framework of continuous speech recognition. The language of the applications we want to deal with, is described using a context-free grammar given in Greibach normal form. The parsing algorithm follows the level-building technique and finds the p sentences matching the speech signal with the best scores. Our approach is different from the existing ones, in the sense that it is suboptimal but with a lower order of complexity. By suboptimal we mean that a syntactically correct sentence with a score belonging to the p best ones can be missed by our algorithm. This leads us to discuss the trade-off between quality of results on the one hand and the complexity of the algorithm on the other hand. As a conclusion, we will see that in practice, our approach yields results of comparable quality in spite of their slight theoritical corruption.