Effective reservoir parameter prediction is important for subsurface characterization and understanding fluid migration. However, conventional methods for obtaining porosity and permeability are based on either core measurements or mathematical/petrophysical modeling, which are expensive or inefficient. In this study, we develop a reliable and low-cost deep learning (DL) framework for reservoir permeability and porosity prediction from real logging data at different regions. We leverage an advanced learning architecture (i.e., the transformer model) and design a new regression network (RPTransformer) that is sensitive to the depth period change of the logging data. The RPTransformer is composed of 1D convolutional, long short-term memory (LSTM), and transformer layers. First, we use a 1D convolutional layer for the first layer of the network to extract significant features from the logging data. Then, the nonlinear mapping relationships between logging data and reservoir parameters are established using several LSTM layers with a period parameter. Afterward, we use the encoder in the vision transformer with the self-attention mechanism to further extract logging data features. The developed network is a data-driven supervised learning framework and indicates highly accurate and robust prediction results when applied to different geographic regions. To demonstrate the reliable prediction performance of our network, we compare it with several classic machine learning and state-of-the-art DL methods, e.g., random forest, multilayer LSTM, and long short-term time-series network (LSTNet). More importantly, we find the generalization and uncertainty of the network in real-world applications through comprehensive numerical experiments.