Real-time electrical spectrum analysis is of great significance for applications involving radio astronomy and electronic warfare, e.g. the dynamic spectrum monitoring of outer space signal, and the instantaneous capture of frequency from other electronic systems. However, conventional electrical spectrum analyzer (ESA) has limited operation speed and observation bandwidth due to the electronic bottleneck. Therefore, a variety of photonics-assisted methods have been extensively explored due to the bandwidth advantage of the optical domain. Alternatively, we proposed and experimentally demonstrated an ultrafast ESA based on all-optical Fourier transform and temporal magnification in this paper. The radio-frequency (RF) signal under test is temporally multiplexed to the spectrum of an ultrashort pulse, thus the frequency information is converted to the time axis. Moreover, since the bandwidth of this ultrashort pulse is far beyond that of the state-of-the-art photo-detector, a temporal magnification system is applied to stretch the time axis, and capture the RF spectrum with 1-GHz resolution. The observation bandwidth of this ultrafast ESA is over 20 GHz, limited by that of the electro-optic modulator. Since all the signal processing is in the optical domain, the acquisition frame rate can be as high as 50 MHz. This ultrafast ESA scheme can be further improved with better dispersive engineering, and is promising for some ultrafast spectral information acquisition applications.