Wavelet analysis has been a powerful tool for exploring and solving many complicated problems in natural science and engineering computation. In this article, the notion of biorthogonal two-direction compactly supported bivariate wavelet packets with polyscale is developed. Their properties is investigated by algebra theory, means of time-frequency analysis methodand, operator theory. The direct decomposition relationship is provided. In the final, new Riesz bases of space are constructed from these wavelet packets. Three biorthogonality formulas regarding these wavelet packets are established.