Real-time optical spectrum analysis is an essential tool in observing ultrafast phenomena, such as the dynamic monitoring of spectrum evolution. However, conventional method such as optical spectrum analyzers disperse the spectrum in space and allocate it in time sequence by mechanical rotation of a grating, so are incapable of operating at high speed. A more recent method all-optically stretches the spectrum in time domain, but is limited by the allowable input condition. 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 frame rate as high as 100 MHz and accommodates various input conditions. As a proof of concept and also for the first time, we verify its applications in observing the dynamic spectrum of a Fourier domain mode-locked laser, and the spectrum evolution of a laser cavity during its stabilizing process.