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In this paper, a new fast algorithm is proposed to suppress inter-carrier interference (ICI) in SISO-OFDM systems. Previous algorithms, due to high computation time, are impractical for OFDM systems especially with large number of subcarriers. To overcome this problem, our proposed algorithm computes rather than K2 elements of carrier frequency offset (CFO) matrix used by previous algorithms, only computes K elements to estimate CFO effect. To estimate CFO matrix, we use the recursive function considered in Fast Independent Component Analysis (FastICA) algorithm. Simulation results show significant decrease in the computation time in comparison with other algorithms. Moreover, they show that by increasing the number of subcarriers, the performance of the system remains almost unchanged.