According to what is written in the New Testament, no. For Paul said the following,
"All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work." (2 Timothy 3:16-17 NKJV)
Note: Paul was referring to the Old Testament, which was otherwise known as the Scriptures (see Mark 14:49; Matthew 26:54; Luke 24:45).
Now then, if Paul (the man who wrote most of the NT) saw the Old Testament as being profitable for all of the things that he had mentioned above, then why would any Christian want to discard it?