Abstract: Based on Orthogonal Polynomial Expansions on the Disk algorithm (OPED), fast reconstruction method of limited angle Radon projections is proposed to cope with the problem of Computed Tomography (CT) in Radon projections. By solving linear system equations to estimate the missing data，Fast Fourier Transform (FFT) and linear interpolation method are applied to reduce the computation time. Derivations and numerical examples for one side and both side limited projection reconstruction are given, respectively. The simulation results show that the proposed method can effectively raise the efficiency of reconstruction.