In this paper, we proposed a closed-form solution for blind Carrier Frequency Offset (CFO) estimation employing the Rank-Revealing QR triangular factorization Method (RRQR) for Multicarrier Modulation system. The advantage of using the RRQR it gives precious information about numerical rank and efficiently separates the signal space from the noise space. Computer simulations are showing the superior performance of RRQR compared with the method employing ESPRIT Algorithm.