We present a forecast analysis on the feasibility of measuring the cosmological parameters with a large number of galaxy-galaxy scale strong gravitational lensing systems. Future wide area surveys are expected to discover and measure the properties of more than 10 000 strong lensing systems. We develop a hierarchical model that can simultaneously constrain the lens population and cosmological parameters by combining Einstein radius measurements with stellar dynamical mass estimates for every lens. Marginalizing over the lens density profiles and stellar orbital anisotropies, we find that \(w\) can be constrained to a precision of \(0.11\) with 10 000 galaxy-galaxy lens systems, which would be better than any existing single-probe constraint. We test our method on 161 existing lenses, finding \(w=-0.96\pm0.46\). We also show how to mitigate against the potential systematic of redshift evolution in the mean lens density profile of the population.