We propose a fast calculation method of a computer-generated hologram (CGH) using an approximate Fresnel integral. Calculating a Fresnel integral requires the calculation of a numerical integral, which consumes computational time. When generating a CGH using a Fresnel integral, it is difficult to calculate it in real-time. Instead of a Fresnel integral, we use an approximate Fresnel integral without a numerical integral. In addition, we use an look-up table with small memory and multi-thread technology on a CPU in order to accelerate the generation of the approximate Fresnel integral. We show a numerical experiment that enables a CGH from a simple scene consisting of rectangular patches to be calculated in real-time on a PC.