Background: Although quantitative myocardial T1 and T2 mappings are clinically used to evaluate myocardial diseases, their application needs a minimum of six breath-holds to cover three short-axis slices. The purpose of this work is to simultaneously quantify multislice myocardial T1 and T2 across three short-axis slices in one breath-hold by combining simultaneous multislice (SMS) with multimapping. Methods: An SMS-Multimapping sequence with multiband radiofrequency (RF) excitations and Cartesian fast low-angle shot readouts was developed for data acquisition. When 3 slices are simultaneously acquired, the acceleration rate is around 12-fold, causing a highly ill-conditioned reconstruction problem. To mitigate image artifacts and noise caused by the ill-conditioning, a reconstruction algorithm based on locally low-rank and sparsity (LLRS) constraints was developed. Validation was performed in phantoms and in vivo imaging, with 20 healthy subjects and 4 patients, regarding regional mean, precision, and scan-rescan reproducibility. Results: The phantom imaging shows that SMS-Multimapping with locally low-rank (LLRS) accurately reconstructed multislice T1 and T2 maps despite a six-fold acceleration of scan time. Healthy subject imaging shows that the proposed LLRS algorithm substantially improved image quality relative to split slice-generalized autocalibrating partially parallel acquisition. Compared with modified look-locker inversion recovery (MOLLI), SMS-Multimapping exhibited higher T1 mean (1118 +/- 43 ms vs 1190 +/- 49 ms, P < 0.01), lower precision (67 +/- 17 ms vs 90 +/- 17 ms, P < 0.01), and acceptable scan-rescan reproducibility measured by 2 scans 10min apart (bias = 1.4 ms for MOLLI and 9.0 ms for SMS-Multimapping). Compared with balanced steady-state free precession (bSSFP) T2 mapping, SMS-Multimapping exhibited similar T2 mean (43.5 +/- 3.3 ms vs 43.0 +/- 3.5 ms, P = 0.64), similar precision (4.9 +/- 2.1 ms vs 5.1 +/- 1.0 ms, P = 0.93), and acceptable scanrescan reproducibility (bias = 0.13 ms for bSSFP T2 mapping and 0.55 ms for SMS-Multimapping). In patients, SMS-Multimapping clearly showed the abnormality in a similar fashion as the reference methods despite using only one breath-hold. Conclusion: SMS-Multimapping with the proposed LLRS reconstruction can measure multislice T1 and T2 maps in one breath-hold with good accuracy, reasonable precision, and acceptable reproducibility, achieving a six-fold reduction of scan time and an improvement of patient comfort.