Carrier Frequency Offset (CFO) is one of the major drawbacks of the Multi Carrier Modulation (MCM) technique. Blind, semiblind and data-aided techniques have been introduced to estimate the CFO. In this paper, a new blind CFO estimator based on the Matrix Pencil (MP) method is proposed. A closed-form solution of this generalized eigenvalue problem using the MP method is solved by Rank Revealing QR factorization (RRQR). The RRQR reveals information about numerical rank and efficiently divides the space into signal and noise subspaces. Our algorithm is proficient to estimate CFO by not involving Eigenvalue Decomposition (EVD) or Singular Value Decomposition (SVD) of the spectral data matrix. The proposed method is characterized by the highly accurate CFO estimation especially with a very small number of OFDM frames. Computer simulations are included to show the dominant performance of our proposed method by comparing it with the ESPRIT algorithm, particularly at lower numbers of available data blocks