Quantification of magnetic resonance parameters plays an increasingly important role in clinical applications, such as the detection and classification of neurodegenerative diseases. The major obstacle that remains for its widespread use in clinical routine is the long scanning times. Therefore, strategies that allow for significant decreases in scan time are highly desired. Recently, the k-t principal component analysis method was introduced for dynamic cardiac imaging to accelerate data acquisition. This is done by undersampling k-t space and constraining the reconstruction of the aliased data based on the k-t Broad-use Linear Acquisition Speed-up Technique (BLAST) concept and predetermined temporal basis functions. The objective of this study was to investigate whether the k-t principal component analysis concept can be adapted to parameter quantification, specifically allowing for significant acceleration of an inversion recovery fast imaging with steady state precession (TrueFISP) acquisition. We found that three basis functions and a single training data line in central k-space were sufficient to achieve up to an 8-fold acceleration of the quantification measurement. This allows for an estimation of relaxation times T(1) and T(2) and spin density in one slice with sub-millimeter in-plane resolution, in only 6 s. Our findings demonstrate that the k-t principal component analysis method is a potential candidate to bring the acquisition time for magnetic resonance parameter mapping to a clinically acceptable level.