Abstract: The purpose of computing first network is to deeply integrate the ubiquitous computation with network, in order to effectively allocate multi-dimensional basic resources such as computation and storage between clouds, edges and ends through the network, allowing users to use them as transparently as water and electricity resources. Computing resources can be requested on demand and used at any time. Due to heterogeneous computing resources, dynamic network and diverse user needs, it has become one of the core challenging problems to effectively schedule and route resources in computing first network. To address this problem, we design a Multi-tier computing resource system(CRS). Different from the existing resource allocation, CRS is a complete computing first network technology solution based on the application layer, considering the computing resources awareness and computational routing. The computing resource system is composed of computing resource awareness strategy and computing resource routing protocol. The computing resource awareness strategy defines the intra-domain awareness rules within the jurisdiction and the inter-domain awareness rules between different jurisdictions. Based on this, we proposed a Greedy-Based Resource Routing Algorithm (GBRA), which can dynamically generate a search tree for each task. The computing resource routing protocol completes the allocation of resources through CRS request message, authorization notification message, notification confirmation message and CRS response message. Through extensive simulation experiments, compared with other algorithms, it is demonstrated that CRS can complete the resource allocation of more tasks within the maximum response latency tolerated. In addition, better load balancing can be achieved among the computing nodes within the jurisdiction.