The continued success in the development of neuromorphic computing has immensely pushed today's artificial intelligence forward. Deep neural networks (DNNs), a brainlike machine learning architecture, rely on the intensive vector-matrix computation with extraordinary performance in data-extensive applications. Recently, the nonvolatile memory (NVM) crossbar array uniquely has unvailed its intrinsic vector-matrix computation with parallel computing capability in neural network designs. In this article, we design and fabricate a hybrid-structured DNN (hybrid-DNN), combining both depth-in-space (spatial) and depth-in-time (temporal) deep learning characteristics. Our hybrid-DNN employs memristive synapses working in a hierarchical information processing fashion and delay-based spiking neural network (SNN) modules as the readout layer. Our fabricated prototype in 130-nm CMOS technology along with experimental results demonstrates its high computing parallelism and energy efficiency with low hardware implementation cost, making the designed system a candidate for low-power embedded applications. From chaotic time-series forecasting benchmarks, our hybrid-DNN exhibits 1.16x- 13.77 x reduction on the prediction error compared to the state-of-the-art DNN designs. Moreover, our hybrid-DNN records 99.03% and 99.63% testing accuracy on the handwritten digit classification and the spoken digit recognition tasks, respectively.