Ultrafast DCE-MRI shows promise for detection of cancers. However, existing simple mathematical models do not have a smooth transition from baseline to early uptake phase and thus do not accurately model the early kinetics. Here we developed a new three-parameter model by combining a 4th-order rational and exponential function, namely REM (rational-exponential-model). Ultrafast prostate DCE-MRI was used to verify the accuracy of REM and compare the REM with two other models. The curvatures during initial enhancement and transition to washout were calculated. The REM characterized contrast agent kinetics for ultrafast DCE-MRI more accurately than previously developed models and thus improved diagnostic accuracy.