Light-in-flight imaging enables the visualization and characterization of light propagation, which provides essential information for the study of the fundamental phenomena of light. A camera images an object by sensing the light emitted or reflected from it, and interestingly, when a light pulse itself is to be imaged, the relativistic effects, caused by the fact that the distance a pulse travels between consecutive frames is of the same scale as the distance that scattered photons travel from the pulse to the camera, must be accounted for to acquire accurate space–time information of the light pulse. Here, we propose a computational light-in-flight imaging scheme that records the projection of light-in-flight on a transverse x?y plane using a single-photon avalanche diode camera, calculates $z$ and $t$ information of light-in-flight via an optical model, and therefore reconstructs its accurate ($x$, $y$, $z$, $t$) four-dimensional information. The proposed scheme compensates the temporal distortion in the recorded arrival time to retrieve the accurate time of a light pulse, with respect to its corresponding spatial location, without performing any extra measurements. Experimental light-in-flight imaging in a three-dimensional space of $375\mathrm{mm}\times 75\mathrm{mm}\times 50\mathrm{mm}$ is performed, showing that the position error is 1.75 mm, and the time error is 3.84 ps despite the fact that the camera time resolution is 55 ps, demonstrating the feasibility of the proposed scheme. This work provides a method to expand the recording and measuring of repeatable transient events with extremely weak scattering to four dimensions and can be applied to the observation of optical phenomena with ps temporal resolution.