Ultrafast optical spectrum monitoring is one of the most challenging tasks in observing ultrafast phenomena, such as the spectroscopy, dynamic observation of the laser cavity, and spectral encoded imaging systems. However, conventional method such as optical spectrum analyzer (OSA) spatially disperses the spectrum, but the space-to-time mapping is realized by mechanical rotation of a grating, so are incapable of operating at high speed. Besides the spatial dispersion, temporal dispersion provided by dispersive fiber can also stretches the spectrum in time domain in an ultrafast manner, but is primarily confined in measuring short pulses. In view of these constraints, here we present a real-time spectrum analyzer called parametric spectro-temporal analyzer (PASTA), which is based on the time-lens focusing mechanism. It achieves a 100-MHz frame rate and can measure arbitrary waveforms. For the first time, we observe the dynamic spectrum of an ultrafast swept-source: Fourier domain mode-locked (FDML) laser, and the spectrum evolution of a laser cavity during its stabilizing process. In addition to the basic single-lens structure, the multi-lens configurations (e.g. telescope or wide-angle scope) will provide a versatile operating condition, which can zoom in to achieve 0.05-nm resolution and zoom out to achieve 10-nm observation range, namely 17 times zoom in/out ratio. In view of the goal of achieving spectrum analysis with fine accuracy, PASTA provides a promising path to study the real-time spectrum of some dynamic phenomena and non-repetitive events, with orders of magnitude enhancement in the frame rate over conventional OSAs.