In this work, we apply transfer learning to improve galaxy redshift (distance) predictions in cosmology. Traditional machine learning models for redshift estimation rely on spectroscopic redshifts, which are precise but only represent a limited sample of galaxies. To make redshift models more generalizable to the broader galaxy population, we explore transfer learning as a method to enhance performance across diverse datasets. We use the COSMOS survey to create a dataset, TransferZ, which includes redshift measurements derived from up to 35 imaging filters. This dataset spans a wider range of galaxy types and colors compared to spectroscopic samples, though its redshift estimates are less accurate. We first train a base neural network on TransferZ and then refine it using transfer learning on a dataset of galaxies with more precise spectroscopic redshifts (GalaxiesML). Our results show that transfer learning improves redshift predictions on both datasets by reducing outlier rates and root mean square error (RMS). While it enhances performance on the more specific GalaxiesML dataset, there is a slight reduction in accuracy on the TransferZ dataset. Overall, transfer learning proves to be more effective than simply combining datasets with different types of ground truth, leading to better model generalization.