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Deep Convolutional Neural Networks (CNN) have evolved as popular machine learning models for image classification during the past few years, due to their ability to learn the problem-specific features directly from the input images. The success of deep learning models solicits architecture engineering rather than hand-engineering the features. However, designing state-of-the-art CNN for a given task remains a non-trivial and challenging task, especially when training data size is less. To address this phenomena, transfer learning has been used as a popularly adopted technique. While transferring the learned knowledge from one task to another, fine-tuning with the target-dependent Fully Connected (FC) layers generally produces better results over the target task. In this paper, the proposed AutoFCL model attempts to learn the structure of FC layers of a CNN automatically using Bayesian optimization. To evaluate the performance of the proposed AutoFCL, we utilize five pre-trained CNN models such as VGG-16, ResNet, DenseNet, MobileNet, and NASNetMobile. The experiments are conducted on three benchmark datasets, namely CalTech-101, Oxford-102 Flowers, and UC Merced Land Use datasets. Fine-tuning the newly learned (target-dependent) FC layers leads to state-of-the-art performance, according to the experiments carried out in this research. The proposed AutoFCL method outperforms the existing methods over CalTech-101 and Oxford-102 Flowers datasets by achieving the accuracy of 94.38% and 98.89%, respectively. However, our method achieves comparable performance on the UC Merced Land Use dataset with 96.83% accuracy. The source codes of this research are available at https://github.com/shabbeersh/AutoFCL.