Brain-on-a-chip, a method for reconstructing neuronal networks with brain-like properties in a cultured environment, has attracted attention for investigating the relationship between connection structure and activity patterns. As fundamental technologies for realizing such devices, bioengineering technologies to reconstruct modular structure and directional connection with living cells have been developed previously, they have not been integrated to realize modular networks with directionality. In this study, we developed a novel microfluidic device to reconstruct such network with cultured cortical neurons and investigated how the network structure influences its dynamics.An asymmetric microchannel with 4-step tapered geometry was fabricated to implement directional connectivity and a pseudo-feedforward structure in a 16-module network. The neurite elongation through the asymmetric microchannel was biased at 82.6% in the forward direction. Furthermore, we found that the probability of activity propagation in the reverse direction, but not in the forward direction, was inhibited by the asymmetric microchannel. Consequently, it was found that implementation of pseudo-feedforward connections in modular neuronal networks reduced excessive synchronization and enriched the spontaneous activity patterns. The observation was well captured in a spiking neural network model with directional and modular connections. Our experimental system revealed that directional connection plays an important role in enhancing the dynamical complexity.The work was partly supported by MEXT Grant-in-Aid for Transformative Research Areas (B) “Multicellular Neurobiocomputing”, JSPS KAKENHI, JST CREST, and Tohoku University RIEC Cooperative Research Project Program.