Non-reciprocal antenna beam patterns are promising to be utilized in asymmetric massive multiple-input multiple-output (MIMO) systems for future sixth-generation communications. The inconsistency of uplink (UL) and downlink (DL) channels makes channel modeling in this scenario challenging. In this paper, a novel geometry-based stochastic model (GBSM) is proposed for non-reciprocal terahertz (THz) channels. A directional effective scatterer generation algorithm is designed to depict the inconsistency of bidirectional propagation conditions. The correlation function between UL and DL is derived and analyzed, which validates the ability to characterize the non-reciprocal channels. To mimic THz propagation features, molecular absorption and diffuse scattering are introduced to the model, which is verified by measured data. In addition, the non-stationarities in space, time, and frequency domains are characterized, respectively. Statistical properties are compared between analytical and simulation results, and good agreements are shown. Finally, the accuracy of the model is verified by comparing with the ray tracing data.