Large-scale Deterministic Network (LDN) is developed to achieve deterministic transmission in large-scale networks, which can provide bounded delay and jitter with the Cycle Specified Queuing and Forwarding (CSQF) and shaping mechanisms. Routing for time-sensitive flows in LDN requires meeting the delay and bandwidth constraints, like the Multi-Constrained Path (MCP) problem. However, there is a discrepancy that the constraints in the MCP problem are definite while in LDN they are uncertain. It is because the flow’s rate can be adjusted by the shaper, which influences the waiting time at the ingress node and reserved bandwidth at the path. We call the routing problem in LDN the Multi Variable Constraints Routing (MVCR) problem. Due to the uncertainty of constraints, existing routing algorithms may encounter overlong runtime or early rejection if applied to the MVCR problem. In this paper, we propose a Heuristic Fast Routing solution to address the MVCR problem in LDN, called HFR-L. Firstly, we establish a pathbook in advance and design a metric for selecting routes from it with taking the variable flow’s rate into consideration. Then, given the possibility of network changes or the absence of feasible paths in pathbook, we design an algorithm to compute routes in real time, which is based on an extended Lagrange Relaxation based Aggregated Cost (LARAC) algorithm and continuously adjusts the flow’s rate to balance the constraints. The experiments show that our HFR-L has excellent routing performance and fast execution speed in both global and online scenarios, confirming its feasibility to be used in LDN.