The loss of limb motion arising from damage to the spinal cord is a disability that could effect people while performing their day-to-day activities. The restoration of limb movement would enable people with spinal cord injury to interact with their environment more naturally and this is where a brain-computer interface (BCI) system could be beneficial. The detection of limb movement imagination (MI) could be significant for such a BCI, where the detected MI can guide the computer system. Using MI detection through electroencephalography (EEG), we can recognize the imagination of movement in a user and translate this into a physical movement. In this paper, we utilize pre-trained deep learning (DL) algorithms for the classification of imagined upper limb movements. We use a publicly available EEG dataset with data representing seven classes of limb movements. We compute the spectrograms of the time series EEG signal and use them as an input to the DL model for MI classification. Our novel approach for the classification of upper limb movements using pre-trained DL algorithms and spectrograms has achieved significantly improved results for seven movement classes. When compared with the recently proposed state-of-the-art methods, our algorithm achieved a significant average accuracy of 84.9% for classifying seven movements.