Recurrent neural networks (RNNs) are powerful in the tasks oriented to sequential data, such as natural language processing and video recognition. However, because the modern RNNs have complex topologies and expensive space/computation complexity, compressing them becomes a hot and promising topic in recent years. Among plenty of compression methods, tensor decomposition, e.g., tensor train (TT), block term (BT), tensor ring (TR), and hierarchical Tucker (HT), appears to be the most amazing approach because a very high compression ratio might be obtained. Nevertheless, none of these tensor decomposition formats can provide both space and computation efficiency. In this article, we consider to compress RNNs based on a novel Kronecker CANDECOMP/PARAFAC (KCP) decomposition, which is derived from Kronecker tensor (KT) decomposition, by proposing two fast algorithms of multiplication between the input and the tensor-decomposed weight. According to our experiments based on UCF11, Youtube Celebrities Face, UCF50, TIMIT, TED-LIUM, and Spiking Heidelberg digits datasets, it can be verified that the proposed KCP-RNNs have a comparable performance of accuracy with those in other tensor-decomposed formats, and even 278 219× compression ratio could be obtained by the low-rank KCP. More importantly, KCP-RNNs are efficient in both space and computation complexity compared with other tensor-decomposed ones. Besides, we find KCP has the best potential of parallel computing to accelerate the calculations in neural networks.