Machining error is one of the most important indicators to evaluate the processing quality of thin-walled parts. With the development of Data Science, the data-driven methods have become popular. But the condition that the model can work accurately on a new task is that the feature space and distribution of the data are the same. A sample-based transfer learning method driven by geometric position is utilized to quickly predict the machining errors of thin-walled parts under different working conditions. This method can fully learn the knowledge related to machining errors contained in the data through model training, and can apply this knowledge to accurately and quickly forecast machining errors under new working conditions. In the experimental scenario, this method has outstanding predictive performance. The average determination coefficient of the four groups of target domain experiments reached 0.96, and the average root mean square error is less than the machining error acquisition time to 22% of the original, reducing the dependence on time-consuming and expensive measurements greatly.