Abstract Purpose. This study aims to investigate the feasibility of different acquisition methods for time-resolved magnetic resonance fingerprinting (TR-MRF) in computer simulation. Methods. An extended cardiac-torso (XCAT) phantom is used to generate abdominal T1, T2, and proton density maps for MRF simulation. The simulated MRF technique consists of an IR-FISP MRF sequence with spiral trajectory acquisition. MRF maps were simulated with different numbers of repetitions from 1 to 15. Three different methods were used to generate TR-MRF maps: (1) continuous acquisition without delay between MRF repetitions; (2) continuous acquisition with 5 s delay between MRF repetitions; (3) triggered acquisition with variable delay between MRF repetitions to allow the next acquisition to start at different respiration phase. After the generation of TR-MRF maps, the image quality indexes including the absolute T1 and T2 values, signal-to-noise-ratio (SNR), tumor-to-liver contrast-to-noise ratio, error in the amplitude of diaphragm motion and tumor volume error were used to evaluate the reconstructed parameter maps. Three volunteers were recruited to test the feasibility of the selected acquisition method. Results. Dynamic MR parametric maps using three different acquisition methods were estimated. The overall and liver T1 value error, liver SNR in T1 and T2 maps, and tumor SNR from T1 maps from triggered method is statistically significantly better than the other two methods (p-value < 0.05). The other image quality indexes have no significant difference between the triggered method and the other two continuous acquisition methods. All image quality indexes exhibit no significant difference between the acquisition methods with 0 s and 5 s delay. The triggered method was successfully performed in three healthy volunteers. Conclusion. TR-MRF technique was investigated using three different acquisition methods in computer simulation where the triggered method showed better performance than the other two methods. The triggered method has been tested successfully in healthy volunteers.