A new parsing algorithm is presented. The algorithm works in a top-down manner and it is easily implementable. The algorithm works for all non left-recursive e-free context-free grammars. For LR(1) left-recursion-free grammars works like an LR(1) push-down acceptor. The time bounds are O(n3) for all context-free grammars, O(n2) for a superset of unambiguous grammars and O(n) for a superset of LR grammars (see Graham, Harrison [1]). It is hoped that the ideas used in the algorithm can help to find an accepting algorithm working in time O(n2). The method has promising properties for error recovery in compilers and produces all the possible parses in a string encoding. In any case, the ideas presented in the paper can contribute to the understanding of the parsing problem of general context-free languages.