Because the measurement techniques using global navigation satellite system (GNSS) have high accuracies, GNSS users can obtain accurate zenith tropospheric delay (ZTD) products. To use GNSS-measured ZTD products, the separation between zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD) is an important step. In this separation step, high accurate ZHD models are required. This study proposes a new ZHD model—the NNSZHD model, specifically designed for the separation between ZHD and ZWD. The development of the NNSZHD model is based on a novel modeling approach, which combines the ZHD values obtained from the direct calculation method and those from the indirect calculation method and is carried out by using an artificial intelligence algorithm. The direct calculation method refers to ZHD values calculated from ZHD model without measured meteorological parameters; while the indirect calculation method refers to ZHD values obtained by subtracting ZWD values (from ZWD model without measured meteorological parameters) from ZTD measurements. Then this study is based on this modeling framework and the GTrop model, which is a state-of-the-art ZTD model without measured meteorological parameters. Three key parameters (ZHDGTrop and ZWDGTrop obtained from the GTrop model, as well as ZTD measurements) are set as the modeling parameters. A multilayer feedforward neural network is used to develop the modeling framework of the NNSZHD model. The NNSZHD model is trained using data from 389 global sounding stations and the evaluation of its accuracy is carried out by using data from an additional 375 stations. The results show that for the region near the surface, the NNSZHD model has an accuracy of 12.35 mm, and its accuracy improves by 3.78 and 3.40 mm respectively compared with the GTrop and GPT2w models. For the tropospheric region with heights below 10 km, the model’s accuracy reaches 7.52 mm, and it shows improvements of respective 7.08 and 35.13 mm compared with the GTrop and GPT2w models. When we can only rely on ZTD models without measured meteorological parameters, the NNSZHD model has significant potential applications in GNSS tropospheric delay corrections and GNSS meteorology.