The advantages of wavelet packets and their promising features in various application have attracted a lot of interest and effort in recent years. In this paper, the concept of biorthogonal two-directional finitely supported wavelet wraps with four-scale is introduced. A new method for designing two-directional biorthogonal wavelet wraps is developed and their properties is investigated by means of time-frequency analysis method, matrix theory and operator theory. The decomposition relationship is established. Finally, two Riesz bases of space L 2 (R 2 )are constructed from these wavelet wraps. The biorthogonal finitely supported bonary wavelet wraps was generalized to two-directional biorthogonal wavelet wraps.