We demonstrate a short-wave infrared computed tomography method. It uses a fiber-coupled 1.44µm super-luminescent diode as light source, a PbSe photodiode as infrared detector, and an electronically controlled rotation and translation stage for high-speed Radon scanning. It is a safe and low power nondestructive testing method that can be used for the detection of plastic polymers, biological tissue and other materials that visible light cannot penetrate. We analyze the theoretical resolution of the method and build a short-wave infrared computed tomography system, which realizes the tomography and 3D reconstruction of black plastic bottles and artificial blood vessels. The measured resolution reaches10µm.