Speech emotion recognition (SER) is an important application in Affective Computing and Artificial Intelligence. Recently, there has been a significant interest in Deep Neural Networks using speech spectrograms. As the two-dimensional representation of the spectrogram includes more speech characteristics, research interest in convolution neural networks (CNNs) or advanced image recognition models is leveraged to learn deep patterns in a spectrogram to effectively perform SER. Accordingly, in this study, we propose a novel SER model based on the learning of the utterance-level spectrogram. First, we use the Spatial Pyramid Pooling (SPP) strategy to remove the size constraint associated with the CNN-based image recognition task. Then, the SPP layer is deployed to extract both the global-level prominent feature vector and multi-local-level feature vector, followed by an attention model to weigh the feature vectors. Finally, we apply the ArcFace layer, typically used for face recognition, to the SER task, thereby obtaining improved SER performance. Our model achieved an unweighted accuracy of 67.9% on IEMOCAP and 77.6% on EMODB datasets.