Magnetic resonance fingerprinting (MRF) is a novel and efficient method for the estimation of MR parameters, such as off-resonance (DB0), proton density (PD), T1 and T2. Because of the highly undersampled readout that is conventionally used, large number of dynamics (e.g. <1000) are often acquired for maintaining the fidelity of MR parameter estimations (a.k.a. dictionary matching). In this study, we propose a new algorithm, MRF reconstruction using majorization-minimization (mmMRF), such that fidelity of dictionary matching can remain similar even when significantly less number of dynamics are available.