In this paper, we propose an acceleration methodology for deep recurrent neural networks (RNNs) implemented on a multi-FPGA platform called Flow-in-Cloud (FiC). RNNs have been proven effective for modeling temporal sequences, such as human speech and written text. However, the implementation of RNNs on traditional hardware is inefficient due to their long-range dependence and irregular computation patterns. This inefficiency manifests itself in the proportional increase of run time with respect to the number of layers of deep RNNs when running on traditional hardware platforms such as a CPUs. Previous works have mostly focused on the optimization of a single RNN cell. In this work, we take advantage of the multi-FPGA system to demonstrate that we can reduce the run time of deep RNNs from O(k) to O(1).