We extend the Hubble diagram up to z = 5.6 using 63 gamma-ray bursts ( GRBs ) via peak energy-peak luminosity relation ( so called Yonetoku relation ) , and obtain constraints on cosmological parameters including dynamical dark energy parametrized by P / \rho \equiv w ( z ) = w _ { 0 } + w _ { a } \cdot z / ( 1 + z ) .
It is found that the current GRB data are consistent with the concordance model , ( \Omega _ { m } = 0.28 , \Omega _ { \Lambda } = 0.72 ,w _ { 0 } = -1 ,w _ { a } = 0 ) , within two sigma level .
Although constraints from GRBs themselves are not so strong , they can improve the conventional constraints from SNeIa because GRBs have much higher redshifts .
Further we estimate the constraints on the dark-energy parameters expected by future observations with GLAST ( Gamma-ray Large Area Space Telescope ) and Swift by Monte-Carlo simulation .
Constraints would improve substantially with another 150 GRBs .