Magnetic resonance fingerprinting (MRF) based on echo-planar imaging (EPI) enables whole-brain imaging to rapidly obtain T1 and T2* relaxation time maps. Reconstructing parametric maps from the MRF scanned baselines by the inner-product method is computationally expensive. We aimed to accelerate the reconstruction of parametric maps for MRF-EPI by using a deep learning model. The proposed approach uses a two-stage model that first eliminates noise and then regresses the parametric maps. Parametric maps obtained by dictionary matching were used as a reference and compared with the prediction results of the two-stage model. MRF-EPI scans were collected from 32 subjects. The signal-to-noise ratio increased significantly after the noise removal by the denoising model. For prediction with scans in the testing dataset, the mean absolute percentage errors between the standard and the final two-stage model were 3.1%, 3.2%, and 1.9% for T1, and 2.6%, 2.3%, and 2.8% for T2* in gray matter, white matter, and lesion locations, respectively. Our proposed two-stage deep learning model can effectively remove noise and accurately reconstruct MRF-EPI parametric maps, increasing the speed of reconstruction and reducing the storage space required by dictionaries.