One-dimensional (1D) novel pentagonal materials have gained significant attention as a new class of materials with unique properties that could influence future technologies. In this report, we studied the structural, electronic, and transport properties of 1D pentagonal PdSe2 nanotubes (p-PdSe2 NTs). The stability and electronic properties of p-PdSe2 NTs with different tube sizes and under uniaxial strain were investigated using density functional theory (DFT). The studied structures showed an indirect-to-direct bandgap transition with slight variation in the bandgap as the tube diameter increased. Specifically, (5 × 5) p-PdSe2 NT, (6 × 6) p-PdSe2 NT, (7 × 7) p-PdSe2 NT, and (8 × 8) p-PdSe2 NT are indirect bandgap semiconductors, while (9 × 9) p-PdSe2 NT exhibits a direct bandgap. In addition, under low uniaxial strain, the surveyed structures were stable and maintained the pentagonal ring structure. The structures were fragmented under tensile strain of 24%, and compression of −18% for sample (5 × 5) and −20% for sample (9 × 9). The electronic band structure and bandgap were strongly affected by uniaxial strain. The evolution of the bandgap vs. the strain was linear. The bandgap of p-PdSe2 NT experienced an indirect–direct–indirect or a direct–indirect–direct transition when axial strain was applied. A deformability effect in the current modulation was observed when the bias voltage ranged from about 1.4 to 2.0 V or from −1.2 to −2.0 V. Calculation of the field effect I–V characteristic showed that the on/off ratio was large with bias potentials from 1.5 to 2.0 V. This ratio increased when the inside of the nanotube contained a dielectric. The results of this investigation provide a better understanding of p-PdSe2 NTs, and open up potential applications in next-generation electronic devices and electromechanical sensors.