We propose a novel dictionary-based reconstruction (DIREC) framework for free-breathing myocardial T1 mapping that simultaneously reduces the acquisition time while compensating for the impact of respiratory and cardiac induced motions and off-resonance effect as well as conventional artifacts. The reconstruction method leads to accurately estimating the signal recovery in T1-weighted images with the artifacts. Furthermore, DIREC based on the dictionary designed with an additional candidate set of off-resonance frequency measured consistent T1 value of myocardium by tackling the off-resonance effect. Its superior performance was demonstrated as compared with the conventional SENSE method in a cohort of healthy subjects.