In the paper, a solution of the time-fractional single-phase-lagging heat conduction problem in finite regions is presented. The heat conduction equation with the Caputo time-derivative is complemented by the Robin boundary conditions. The Laplace transform with respect to the time variable and an expansion in the eigenfunctions series with respect to the space variable was applied. A method for the numerical inversion of the Laplace transforms was used. Formulation and solution of the problem cover the heat conduction in a finite slab, hollow cylinder and hollow sphere. The effect of the fractional order of the Caputo derivative and the phase-lag parameter on the temperature distribution in a slab has been numerically investigated.