In this paper, we study the ？rst-order system least- squares (FOSLS) spectral method for parabolic partial di®erential equations. There were lots of least-squares approaches to solve elliptic partial di®erential equations using ？nite element approxi- mation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial di®eren- tial equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and ？rst-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic prob- lems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the ？rst-order sys- tem least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.