This paper treats a winner determination problem of a Vickrey-Clarke-Groves mechanism based single-item multi-unit auction. For this problem, two simple 2-approximation algorithms are proposed. One is a linear time algorithm using a linear knapsack problem. The other is a greedy type algorithm. In addition, a fully polynomial time approximation algorithm based on a dynamic programming is described. Computational experiments verify availabilities of our algorithms by comparing computational times and approximation ratios.