In this talk we present the recent development of Finite Integration Method (FIM) for solving multi-dimensional partial differential equations. The main idea is to extend the first order finite integration matrices constructed by using either Ordinary Linear Approach (FIM-OLA) (uniform distribution of nodes) or Radial Basis Function (FIM-RBF) (non-uniform distribution of nodes) to higher order integration matrices. Using standard time integration techniques, such as Laplace transformation, we demonstrate that the FIM is capable to solve time-dependent multi-dimensional partial differential equations. Numerical examples in two-dimension are given to demonstrative the superior accuracy and efficiency of both FIM-OLA and FIM-RBF in comparing with Finite Difference Method and Meshless Collocation Method.