First-pass contrast-enhanced myocardial perfusion imaging is valuable for evaluating coronary artery disease (CAD). Spiral perfusion imaging techniques, using a motion-compensated L1-SPIRiT based reconstruction, are capable of whole-heart high-resolution perfusion imaging. However, this reconstruction is performed off-line and takes ~1 hour per slice. To address this limitation, we developed a DEep learning-based Spiral Image REconstruction technique (DESIRE) for spiral first-pass myocardial perfusion imaging, for both single-slice (SS) and simultaneous multi-slice (SMS) MB=2 acquisitions, to provide fast and high-quality image reconstruction and make rapid online reconstruction feasible. High image quality was demonstrated using the proposed technique for healthy volunteers and patients.