Better Translation is "Be anxious for nothing..." I.E. fear for nothing. The scripture is telling us, rather than be anxious and full of fear, take it to God in prayer, and what is the result of taking it to God in prayer? It's the next verse, "and the peace of God, which surpasses all understanding, will guard your hearts and minds through Christ Jesus."

God will provide the peace for your heart, in other words, He will give you peace to replace the fear.