We use the H II galaxies L–σ relation and the resulting Hubble expansion cosmological probe of a sample of just 25 high-z (up to z ∼ 2.33) H II galaxies, in a joint likelihood analysis with other well tested cosmological probes (cosmic microwave background, CMB, Baryon Acoustic Oscillations, BAOs) in an attempt to constrain the dark energy equation of state (EoS). The constraints, although still weak, are in excellent agreement with those of a similar joint analysis using the well established SNIa Hubble expansion probe. Interestingly, even with the current small number of available high redshift H II galaxies, the H II/BAO/CMB joint analysis gives a 13 per cent improvement of the quintessence dark energy cosmological constraints compared to the BAO/CMB joint analysis. We have further performed extensive Monte Carlo simulations, with a realistic redshift sampling, to explore the extent to which the use of the L–σ relation, observed in H II galaxies, can constrain effectively the parameter space of the dark energy EoS. The simulations predict substantial improvement in the constraints when increasing the sample of high-z H II galaxies to 500, a goal that can be achieved in reasonable observing times with existing large telescopes and state-of-the-art instrumentation.