As medical CT images always have blurred edges, low contrast, and noise pollution, etc., a new method based on Short-time Fractional Fourier Transform (STFrFT) and infinite-norm is proposed to detect edges of CT images. The imaginary part of STFrFT domain represents the local feature of non-stationary signal. At first, transform the non-stationary signal to STFrFT domain by short-time fractional Fourier transform. Then, obtain the vector infinite norm of STFrFT domain. Two dimensional time-frequency plane is mapped to a one-dimensional signal which shows the edges of the non-stationary signal. Experiment results demonstrate that the proposed method reveals a remarkable performance in detecting the edges of CT images, as well as weak edges. Compared with the results of differential operators and wavelet transform, the proposed approach performs better in the edge detection of CT images and is robust with noise.