Most of studies on network capacity are based on the assumption that all the nodes are uniformly distributed, which means that the networks are characterized by homogeneity. However, many realistic networks exhibit inhomogeneity due to natural and man-made reasons. In this work, the capacity of inhomogeneous hybrid networks with directional antennas for the first time is studied. By setting different node distribution probabilities, the whole network can be devided into dense cells and sparse cells. On this basis, an inhomogeneous hybrid network model is proposed. The network can exhibit significant inhomogeneity due to the coexistence of two types of cells. Then, we derive the network capacity and maximize the capacity under different channel allocation schemes. Finally, how the network parameters influence the network capacity is analyzed. It is found that if there are plenty of base stations, the per-node throughput can achieve constant order, and if the beamwidth of directional antenna is small enough, the network capacity can scale.