Based on terahertz time domain spectroscopy, a false-color imaging system is demonstrated by experiments. Three frequency ranges are defined as color ranges for three primary colors (red, green and blue). The mixture of the spectral integral values in each color range presents the final color of each pixel on the false-color THz image. Since the absorption frequencies of different materials are different, the spectral integral values in defined ranges are different, leading to different color on the false-color THz image. The false-color THz images of two kinds of white powder which are lactose and 4-aminobenzonic acid are obtained from the imaging system with two different definitions of color ranges. From the first color range definition, the absorption frequency of lactose lies in the green range, so only the green light is absorbed, and the color of lactose is magenta. In the meanwhile, there are two absorption frequencies for 4-aminobenzonic acid lying in the green and blue ranges, so both green and blue light are absorbed, and the color of 4-aminobenzonic acid is red. They can be told easily by different colors on the false-color THz image. From the second color range definition, the colors of two kinds of powder are more different. Both false-color THz images can present the cuvette and two kinds of powder clearly. By comparing the THz imaging with grayscale images, false-color THz imaging can display different materials by different colors in one image, instead of the requirement of many grayscale images. It is no need to generate grayscale images at each frequency, making false-color THz imaging consume less time. The false-color imaging is clearer and more efficient, which is more suitable for recognition in a rapid security check. In the situation of complex materials, more false-color THz images can be generated by different color range definitions to assist the detection. The spatial resolution of the imaging system is also investigated. The resolution of imaging system is investigated by imaging home-made standard sample plate. For the frequency range that is higher than 0.3 THz, the resolution can reach 0.4 mm, which is larger than enough for most practical applications.