Tensor-polarized parton distribution functions (PDFs) are calculated for the deuteron by using a convolution formalism, where the tensor-polarized PDFs are given by the corresponding nucleon’s unpolarized PDFs convoluted with the tensor-polarized nucleon momentum distribution in the deuteron. These distributions are obtained at $Q^2=2.5$ GeV${}^2$ in order to compare with the tensor-polarized PDFs which were determined by HERMES $b_1$ data. The obtained distributions are very different from the ones determined from the HERMES data, which indicates further studies are needed to clarify the difference, possibly by considering a new mechanism beyond the simple bound system of a proton and a neutron. The obtained PDFs $_T q $ and ${\delta }_T\bar{q}$ are converted to the PDFs of the Trento convention $f_{1LL}^q$ and $f_{1LL}^{\bar{q}}$, and they are used for estimating the twist-3 PDFs $f_{LT}^q$ and $f_{LT}^{\bar{q}}$ by using a Wandzura-Wilczek-like relation. Because deep-inelastic-scattering experiments are under preparation for structure functions with a tensor-polarized deuteron target at the Thomas Jefferson National Accelerator Facility, and a Drell-Yan experiment will be possible at hadron accelerator facilities, such as the Fermi National Accelerator Laboratory, the obtained tensor-polarized PDFs will be tested experimentally.