Besides energy restriction, wireless sensor networks (WSNs) should be able to provide bounded end-to-end delay when they are used to support real-time applications such as early forest fire alarm systems. In this paper, we investigate the problem of finding the least energy consumption route subject to a delay constraint with low computational complexity in such networks. Based on the distance-vector routing approach, which has less computational complexity and message overhead, we propose a distributed heuristic algorithm called Delay Constrained Energy Efficient Routing (DCEER) in order to minimize the total energy consumption while meeting the end-to-end delay requirement. DCEER only requires a moderate amount of information at each sensor node and does not suffer from the excessive running time. We prove that our proposed algorithm always finishes within a finite time and the computation complexity is only O(n), where n is a divisor of the number of sensor nodes. By mathematical proof and simulation, we verify that DCEER is suitable for large-scale WSNs because the number of messages exchanged between sensor nodes are represented by a polynomial function. Furthermore, we evaluate our proposal to compare its performance with related protocols.