Terahertz (THz) communication is envisioned as one of the possible technologies for the sixth-generation (6G) communication system due to its rich spectrum. To evaluate the performance of THz communication, it is essential to propose THz channel models within the common framework of the geometry-based stochastic model (GBSM) in the 3rd Generation Partnership Project (3GPP). This paper focuses on THz channel modeling and simulation by a 3GPP-like GBSM, based on channel measurements. We first present channel measurements at 100 GHz in an indoor office scenario and 132 GHz in an urban microcellular scenario. Subsequently, channel characteristics such as path loss, delay spread, angle spread, K-factor, cluster characteristic, cross-correlations, and correlation distances are obtained and analyzed based on channel measurement. Additionally, the channel characteristics are modeled by the statistical distribution of 3GPP channel models, which can be used to reconstruct the channel impulse response (CIR). Furthermore, these obtained distributions are studied referring to the default models in the 3GPP, revealing the channel sparsity in the THz channel. For instance, in the case of line-of-sight links in the indoor office, the mean of the measured cluster number is 4 while the default value is 15. Finally, we propose the THz channel model and its simulation framework to reconstruct CIRs based on the obtained models, which aim at characterizing the sparser THz channels. The obvious channel sparsity is characterized in both scenarios, as the Gini factors obtained by the proposed model only have the maximum deviation of 0.04 for those of the measurement. Overall, these findings are helpful in understanding and modeling the THz channel, facilitating the application of THz communication techniques for 6G.