Abstract: To handle the small sample support problem under the heterogeneous clutter environment, a fast convergence Space-Time Adaptive Processing (STAP) algorithm based on low-rank approximation of the weight matrix is proposed. Unlike the traditional Low-Rank Approximation (LRA) algorithm for STAP, the weight matrix is reconstructed so that the numbers of its columns and rows are the same or close to each other by utilizing the special Kronecker property of the space time steering vector, which to reduce the requirement of samples and computational load. By using the low-rank approximation method to approximate the adaptive weight matrix, the original quadratic optimal problem transforms into a bi-quadratic optimal problem. Experimental results verify that the Improved LRA (ILRA) method can improve the convergence rate and reduce the computational load.