Odometer has been proven to significantly improve the robustness and accuracy of the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) integrated vehicle navigation in GNSS-denied environments. However, odometer is inaccessible in many applications, especially for aftermarket devices and smartphones. To apply forward speed aiding without hardware wheeled odometer, we propose OdoNet, an untethered one-dimensional Convolution Neural Network (CNN)-based pseudo-odometer model learning from a single Inertial Measurement Unit (IMU). Dedicated experiments have been conducted to verify the generalization capability and the precision of the OdoNet. The results indicate that the IMU individuality, the vehicle loads, and the road conditions have little impact on the robustness and precision of the OdoNet, while the IMU biases and the mounting angles may notably ruin the OdoNet. Hence, a data-cleaning procedure is adopted to effectively mitigate the impacts of the IMU biases and the mounting angles. Compared to the processing mode using only non-holonomic constraint (NHC), by employing the pseudo-odometer, the positioning error is reduced by around 68%, while the percentage is around 74% for the hardware wheeled odometer. In conclusion, the proposed OdoNet can be employed as an untethered pseudo-odometer for vehicle navigation.