Due to the difficulty in determining the structure and training the parameters of recurrent neural network (RNN), an incremental-construction random RNN (IRRNN) is proposed to realize the incremental construction of RNN structures and the random learning of network parameters. The IRRNN establishes an incremental constraint mechanism for hidden nodes and uses the candidate node pool strategy to realize the optimal selection of hidden nodes, avoiding the blindness of random construction of the network. Two incremental random learning methods, termed IR-1 and IR-2, are designed for local and global optimization of model parameters. Additionally, their universal approximation property is proved. Meanwhile, the dynamic property of the IRRNN model is studied to analyze its generalization performance. Experiments validated that the IRRNN exhibits favorable dynamic properties, compactness, and accuracy.