The purpose of this paper is to find solutions to the 1-median and 2-median problems on a tree network with grey parameters. Generally, the p-median problem asks for finding a set of p facilities on the vertices of a given tree such that the sum of weighted distances from vertices to the closest facility is minimized. First, the 1-median problem with grey weight of vertices and edge lengths is considered, and by showing some properties for this problem, a linear time algorithm is proposed. Then an edge deletion method with time complexity $O(n^2)$ is developed to find a solution to the 2-median problem with grey parameters. Moreover, some new concepts of networks with grey parameters are defined in this paper.