Jesus was a piety Jew in his time, a Law observer, worried about fulfilling the God`s will. Realizing the relationship between Jesus and the Law help us how to understand the situation of his followers communities on Palestine, in constant confrontation with other proposals of faithfulness to the Torah. This dissertation proposes an exegetical- theological analysis on Matthew 5,17-20 to understand this relationship between Jesus and the Law, the way he fulfilled it, and which demands he made from his own practice. The Jesus saying, that he came to fulfill, have already caused every kind of interpretation an the fact of being in the speech`s center known as Sermon on the Mount just increases the interest for it. With the historical-critical method and still the criteria elaborated to the Historical Jesus research, it is possible to do an approach of the text at same time scientific and piety, legitimately interested on the statements of whom is considered the greatest leader of all times.