We propose a heterogeneous on-chip interconnection aiming at high efficiency multicore processors. An ideal on-chip interconnection should have low latency, high throughput, low power consumption, and high scalability. However, these metrics are usually contradictory with each other. Besides, a design should focus on the requirements of real applications. We investigate the characteristics of several parallel applications. It is found that the distribution of traffic is similar as the power law. We also discovered hot spot traffic, as well as bursty traffic from applications.Meanwhile, the average injection rate of parallel applications is relatively low. The proposed network is based on a dual-net concentrated mesh, where 2 physical networks are implemented for processing different messages and improve throughput. A diagonal interconnection is used in the central part of the network for alleviating the traffic hot spot without significant hardware overhead. We evaluate the proposed design with synthetic traffic and real applications by using a simulator. Results indicate that, on average for 8 applications, the network latency of the proposed design has reduced by 32% compared with regular mesh. Concerning efficiency when executing applications, the average energy delay product of the proposed design is 52.7% and 29.7% better than mesh and concentrate mesh, respectively.