X-ray tomography is a powerful method for visualizing the three-dimensional structure of an object with a high spatial resolution. Conventional time-resolved x-ray tomography using synchrotron radiation requires fast rotation of the object, which limits the temporal resolution and hampers its application to, e.g., fluids and in vivo observation of living beings. Here, we present a multibeam x-ray optical system for high-speed 4D tomography, which can obtain projection images of a sample in a wide angular range simultaneously. It consists of about three dozen single-crystalline blades oriented with different angles to the incident beam, which each Bragg-reflect a part of the incident x-rays in the direction of the sample position. Thirty-two projection images covering an angular range of more than ±70◦ were obtained without moving the sample or optical system, with an exposure time of 1 ms. The data set was successfully used for reconstructing the three-dimensional structure of two test samples. The optical system provides the basis for realizing millisecond time resolution x-ray tomography of nonrepeatable phenomena, and can be expected to be useful for other applications as well, for example, for time-resolved element-specific imaging.