The Fractional Fourier transform (FRFT) is the generalization of classical Fourier transform. It can analyze the signal in between the time and frequency domain. The most possible application of the FRFT are optical signal processing, quantum mechanics, optimal filtering. We defined two-dimensional Offset Fractional Fourier transform.The Offset Fractional Fourier transform is the space shifted frequency modulated version of original one. Aim of this paper this paper to present two-dimensional Offset Fractional Fourier transform of some signals.