Dynamic susceptibility contrast magnetic resonance perfusion (DSC-MRP) is a non-invasive imaging technique for hemodynamic measurements. Various perfusion parameters, such as cerebral blood volume (CBV) and cerebral blood flow (CBF), can be derived from DSC-MRP, hence this non-invasive imaging protocol is widely used clinically for the diagnosis and assessment of intracranial pathologies. Currently, most institutions use commercially available software to compute the perfusion parametric maps. However, these conventional methods often have limitations, such as being time-consuming and sensitive to user input, which can lead to inconsistent results; this highlights the need for a more robust and efficient approach like deep learning. Using the relative cerebral blood volume (rCBV) and relative cerebral blood flow (rCBF) perfusion maps generated by FDA-approved software, we trained a multistage deep learning model. The model, featuring a combination of a 1D convolutional neural network (CNN) and a 2D U-Net encoder-decoder network, processes each 4D MRP dataset by integrating temporal and spatial features of the brain for voxel-wise perfusion parameters prediction. An auxiliary model, with similar architecture, but trained with truncated datasets that had fewer time-points, was designed to explore the contribution of temporal features. Both qualitatively and quantitatively evaluated, deep learning-generated rCBV and rCBF maps showcased effective integration of temporal and spatial data, producing comprehensive predictions for the entire brain volume. Our deep learning model provides a robust and efficient approach for calculating perfusion parameters, demonstrating comparable performance to FDA-approved commercial software, and potentially mitigating the challenges inherent to traditional techniques.