Abstract: Based on the non-Fourier heat conduction theory, the spherically symmetric transient heat conduction problem is analyzed in both frequency domain and time domain. By using the Laplace transform and the state-space formula in the frequency domain along with the laminated approximation model, the time responses are obtained numerically through the inverse Laplace transform. This approach is straightforward and with a unified form. For the analysis in the time domain, a combination of the method of separation of variables and the superposition method is adopted, without requiring the numerical inverse Laplace transform. Numerical results indicate that the analysis in the time domain can clearly capture the wave front of the thermal waves.