The magnetization-prepared rapid gradient-echo (MP-RAGE) sequence is well known and widely used for high-resolution, structural brain MRI. Here we present a new version, termed magnetization-prepared spiral acquisition gradient-echo (MP-SAGE), that employs interleaved square-spiral phase-encoding (PE) to take advantage of the 3D nature of the sequence. Resolution loss caused by point-spread function (PSF) blurring is circumvented by the use of variable flip angle (VFA) radiofrequency (RF) pulses. The pulse train is calculated by means of an accurate new signal evolution theory that is derived from the extended phase graph (EPG) description. Phantom results show excellent agreement between theory and experiment for substances with relaxation times similar to those of human brain tissue. Both phantom and in vivo results show a strong enhancement of SNR and CNR compared to the standard MP-RAGE in high-resolution MRI. The benefits for brain tissue segmentation using images obtained with MP-SAGE are shown.