In this paper, transient thermal fracture problem corresponding to non-Fourier heat conduction theory in a semi-infinite medium with a surface crack is studied. By Laplace transform and Laplace inverse transform, the analytical solution of the temperature field is obtained. The thermal stress on the crack surface is performed by virtue of the temperature field obtained and superposition method. The thermal stress intensity factor is given in numerical integration form. Crack propagation behavior is discussed and comparison of the results from the Fourier and non-Fourier heat conduction models is also made. It is found that the non-Fourier model is safer than the Fourier model in predicting the thermal shock fracture strength of brittle media.