We report on the magnetic, electrical transport, and thermal properties of ${\mathrm{Ho}}_{2}{\mathrm{Re}}_{3}{\mathrm{Si}}_{5}$ single crystal by means of magnetization, electrical resistivity, and heat capacity measurements in the temperature range 2--300 K. Magnetic susceptibility, heat capacity, and electrical resistivity reveal two closely spaced antiferromagnetic transitions at ${T}_{\mathrm{N}1}\ensuremath{\sim}$ 3.8 K and ${T}_{\mathrm{N}2}\ensuremath{\sim}$ 4.2 K. Three field-induced metamagnetic transitions at 4.5, 10, and 15 kOe, in the magnetically ordered state at 2 K, have been observed, in the isothermal magnetization, for ${\ensuremath{\mu}}_{0}H\ensuremath{\parallel}c$, and their first-order nature is evident from the magnetic hysteresis. The hysteresis disappears and metamagnetic transitions become feeble at around 3.5 K. These metamagnetic transitions are consistent with field-induced magnetic phases as observed in the magnetic susceptibility, electrical resistivity, and heat capacity. The magnetization for ${\ensuremath{\mu}}_{0}\phantom{\rule{0.16em}{0ex}}H\ensuremath{\parallel}\phantom{\rule{0.16em}{0ex}}a$ is linear without any signature of metamagnetic transition for fields up to 70 kOe suggesting the hard axis of magnetization. From the temperature dependence of the isothermal magnetization, we have constructed a magnetic phase diagram, which signals a complex magnetic structure in this compound. These results suggest that magnetic and transport properties are highly sensitive to the external magnetic field.