For an analytical expression of Vandermonde inverse matrix, a new derivation process based on Wronskian matrix and Lagrange interpolation polynomial basis is presented. Recursive formula and implementation cases for the direct formula of Vandermonde inverse matrix are given based on deriving the unified formula of Wronskian inverse matrix. For the calculation of symbol-type Vandermonde inverse matrix, the direct formula and recursive method are verified to be more efficient than Mathematica which is good at symbolic computation by comparing the computing time in Mathematica. The process and steps of recursive algorithm are relatively simple. The derivation process and idea both have very important values in theory and practice of Vandermonde and generalized Vandermonde inverse matrix.