Abstract: One of the open problems in the graph theory is to find the minimum number of edges required for a graph of order n. A class of graphs with connectivity of at least k and k-diameter of at most d is studied in this paper, and an upper and a lower bound of the minimum edges of the graphs under general conditions are offered. Based on this, the calculation formulas of the minimum edges in two specific situations are also given. In addition we suggest the approaches to costruct the minimum networks as mentioned above.