We suggest a method of bottleneck diagnosis with more excellent performance. There are some problems with current diagnosis methods, such as extra network packets and sensitivity to time changes. In this paper, for UDP network, we propose a new method of bottleneck diagnosis based on the concept of network utility maximization. This bottleneck diagnosis method overcomes the disadvantages of current methods, since it totally depends on mathematic models and method, instead of sending and processing large numbers of packets. The problem is modeled as a geometric program problem and the link loss rates are computed by solving the maximization problem. In addition, the method is expanded to random input rates, allowing network managers to control the network performance more flexibly. At last, experiments are carried out to compare the new method with the method proposed by Shetty et al [1]. The results indicate that our method has better performance in both networks with fixed rates and with random rates.