In this study, a simple spectral-finite volume approach for hyperbolic heat conduction problems under periodic surface temperature is presented. In this approach, by choosing only three frequencies from a continuum frequency spectrum of the periodic temperature field, the time dependent governing equation is transformed into the steady state one in the frequency domain. Then, using the finite volume technique, temperature field in the frequency domain for each wave number is obtained. Finally, by transforming back the result to the time domain, the temperature field in the time domain would be obtained. This new method has been validated against some published results and a good agreement has been found. Despite the simplicity of the present method, it is able to accurately predict the temperature distribution in the periodic steady state portion of non-Fourier heat conduction problems subjected to periodic surface temperature.