We developed a fast method to obtain T1 relaxation maps in magnetic resonance imaging (MRI) based on two inversion recovery acquisitions and a reference acquisition, while maintaining high sensitivity by utilizing the full dynamic range of the MRI signal. Optimal inversion times for estimating T1 in the human brain were predicted using standard error propagation theory. In vivo measurements on nine healthy volunteers yielded T1 values of 1094+/-18 ms in gray matter and 746+/-40 ms in white matter, in reasonable agreement with literature values using conventional approaches. The proposed method should be useful for clinical studies because the T1 maps can be obtained within a few seconds.