The high-temperature deformation mechanisms and processing maps of an equiatomic body-centered-cubic(BCC) structured MoNbHfZrTi refractory high-entropy alloy (RHEA) were studied over the temperatures ranging from 1100 to 1250 °C and different strain rates varying from 10−3 to 0.5 s−1. Flow-stress analyses were performed, using an Arrhenius type relation. The activation energy (Q) for high-temperature deformation was calculated as 326.1 kJ/mol, and the related strain rate sensitivity (m), the power dissipation (η), and instability parameter (ξ) were also derived. The optimal processing area was at 1110–1170 °C and 10−3–10−2.5s−1, with only one unstable region. Detailed microstructural analyses including the surface cracks were carried out in both stable and unstable regions to confirm the derived. Dynamically recrystallized grains with necklace morphologies were observed along grain boundaries and shear bands, indicating that softening was caused by dynamic recrystallization (DRX). The size and proportion of the DRX grains increase with the strain rate decreasing and the temperature increasing.