Purpose: To evaluate the accuracy and repeatability of a free-breathing, non-electrocardiogram (ECG), continuous myocardial T-1 and extracellular volume (ECV) mapping technique adapted from the Multitasking framework. Methods: The Multitasking framework is adapted to quantify both myocardial native T-1 and ECV with a free-breathing, non-ECG, continuous acquisition T-1 mapping method. We acquire interleaved high-spatial resolution image data and high-temporal resolution auxiliary data following inversion-recovery pulses at set intervals and perform low-rank tensor imaging to reconstruct images at 344 inversion times, 20 cardiac phases, and 6 respiratory phases. The accuracy and repeatability of Multitasking T-1 mapping in generating native T-1 and ECV maps are compared with conventional techniques in a phantom, a simulation, 12 healthy subjects, and 10 acute myocardial infarction patients. Results: In phantoms, Multitasking T-1 mapping correlated strongly with the gold-standard spin-echo inversion recovery (R-2 = 0.99). A simulation study demonstrated that Multitasking T-1 mapping has similar myocardial sharpness to the fully sampled ground truth. In vivo native T-1 and ECV values from Multitasking T-1 mapping agree well with conventional MOLLI values and show good repeatability for native T-1 and ECV mapping for 60 seconds, 30 seconds, or 15 seconds of data. Multitasking native T-1 and ECV in myocardial infarction patients correlate positively with values from MOLLI. Conclusion: Multitasking T-1 mapping can quantify native T-1 and ECV in the myocardium with free-breathing, non-ECG, continuous scans with good image quality and good repeatability in vivo in healthy subjects, and correlation with MOLLI T-1 and ECV in acute myocardial infarction patients.