Seismic trace interpolation is an important technique because irregular or insufficient sampling data along the spatial direction may lead to inevitable errors in multiple suppression, imaging, and inversion. Many interpolation methods have been studied for irregularly sampled data. Inspired by the working idea of the autoencoder and convolutional neural network, we have performed seismic trace interpolation by using the convolutional autoencoder (CAE). The irregularly sampled data are taken as corrupted data. By using a training data set including pairs of the corrupted and complete data, CAE can automatically learn to extract features from the corrupted data and reconstruct the complete data from the extracted features. It can avoid some assumptions in the traditional trace interpolation method such as the linearity of events, low-rankness, or sparsity. In addition, once the CAE network training is completed, the corrupted seismic data can be interpolated immediately with very low computational cost. A CAE network composed of three convolutional layers and three deconvolutional layers is designed to explore the capabilities of CAE-based seismic trace interpolation for an irregularly sampled data set. To solve the problem of rare complete shot gathers in field data applications, the trained network on synthetic data is used as an initialization of the network training on field data, called the transfer learning strategy. Experiments on synthetic and field data sets indicate the validity and flexibility of the trained CAE. Compared with the curvelet-transform-based method, CAE can lead to comparable or better interpolation performances efficiently. The transfer learning strategy enhances the training efficiency on field data and improves the interpolation performance of CAE with limited training data.