Ultrafast imaging can capture the dynamic scenes with a nanosecond and even femtosecond temporal resolution. Complementarily, phase imaging can provide the morphology, refractive index, or thickness information that intensity imaging cannot represent. Therefore, it is important to realize the simultaneous ultrafast intensity and phase imaging for achieving as much information as possible in the detection of ultrafast dynamic scenes. Here, we report a single-shot intensity- and phase-sensitive compressive sensing-based coherent modulation ultrafast imaging technique, shortened as CS-CMUI, which integrates coherent modulation imaging, compressive imaging, and streak imaging. We theoretically demonstrate through numerical simulations that CS-CMUI can obtain both the intensity and phase information of the dynamic scenes with ultrahigh fidelity. Furthermore, we experimentally build a CS-CMUI system and successfully measure the intensity and phase evolution of a multimode Q-switched laser pulse and the dynamical behavior of laser ablation on an indium tin oxide thin film. It is anticipated that CS-CMUI enables a profound comprehension of ultrafast phenomena and promotes the advancement of various practical applications, which will have substantial impact on fundamental and applied sciences.