The Mars Sample Return mission is being planned to return samples of Martian rock, regolith, and atmosphere to Earth for scientific analysis. The Martian sample size is directly affected by the propulsion capabilities of the Mars Ascent Vehicle (MAV) and innovations are sought to enhance propulsion capabilities of the MAV for functions including primary propulsion from the Mars surface, orbit insertion, and attitude control. The proposed constant-volume combustion rocket (CVC) propulsion technology will lead to 1) significant weight reduction and simplification; 2) reduced costs in the system components and ground servicing; 3) prolonged mission or systems lifetimes; 4) improved reliability; and 5) enhanced critical mission functions. The Constant Volume Combustion (CVC) engine is an innovative design that combines light weight, low pressure fuel tanks and operates at high chamber pressures. The CVC engine has nearly identical specific impulse as the constant pressure engine with the same mass flow and throat area, furthermore, the nozzle optimizes at the same area ratio. It has exceptional thrust-to-weight ratios, and the proposed bipropellant system meets Martian temperature requirements without heating or stirring. During Phase 1 we will demonstrate, through analysis, experimentation, and hot-fire testing, the feasibility of our proposed CVC engine as a credible candidate for Mars Ascent Propulsion. In Phase II, there will be an aggressive push towards flight-like hardware to ensure rapid maturation of the technology in order to meet the NASA mission goals.