A real-time random grating sensor array for quasi-distributed sensing based on spectral-shaping and wavelength-to-time (SS-WTT) mapping and time-division multiplexing is proposed and experimentally demonstrated. The sensor array consists of multiple random gratings written in a single-mode fiber (SMF) at different physical locations. When the temperature or strain applied to a particular random grating is changed, the central wavelength of the reflection spectrum of the random grating will change, which is converted to the time domain as a time shift based on SS-WTT using a linearly chirped fiber Bragg grating. After detection at a photodetector, an electrical waveform with the time shift information encoded in the random waveform is obtained, which is further compressed by correlation to increase the time resolution. As a demonstration, a real-time quasi-distributed sensing system based on a two-random-grating array is implemented. The results show that the sensing resolutions for temperature and strain are 0.23°C and 2.5 μϵ, respectively, and the accuracies for temperature and strain are 0.11°C and 1.2 μϵ, respectively. Compared with a conventional quasi-distributed sensor, our proposed sensing system has key advantages, including real-time sensing, high-resolution interrogation, and large scalability.